This paper studies the inference problem of index coefficient in single-index models under massive dataset.Analysis of massive dataset is challenging owing to formidable computational costs or memory requirements.A na...This paper studies the inference problem of index coefficient in single-index models under massive dataset.Analysis of massive dataset is challenging owing to formidable computational costs or memory requirements.A natural method is the averaging divide-and-conquer approach,which splits data into several blocks,obtains the estimators for each block and then aggregates the estimators via averaging.However,there is a restriction on the number of blocks.To overcome this limitation,this paper proposed a computationally efficient method,which only requires an initial estimator and then successively refines the estimator via multiple rounds of aggregations.The proposed estimator achieves the optimal convergence rate without any restriction on the number of blocks.We present both theoretical analysis and experiments to explore the property of the proposed method.展开更多
Many of the best predictors for complex problems are typically regarded as hard to interpret physically.These include kernel methods,Shtarkov solutions,and random forests.We show that,despite the inability to interpre...Many of the best predictors for complex problems are typically regarded as hard to interpret physically.These include kernel methods,Shtarkov solutions,and random forests.We show that,despite the inability to interpret these three predictors to infinite precision,they can be asymptotically approximated and admit conceptual interpretations in terms of their mathe-matical/statistical properties.The resulting expressions can be in terms of polynomials,basis elements,or other functions that an analyst may regard as interpretable.展开更多
We would like to thank the authors(Bayarri et al.,2018)for their interesting and provoking paper,and we wish to discuss some issues related to sample size in general and the number of covariates in the context of line...We would like to thank the authors(Bayarri et al.,2018)for their interesting and provoking paper,and we wish to discuss some issues related to sample size in general and the number of covariates in the context of linear regression model when using the Bayesian information criteria(BIC)for model selection.Schwarz(1978)was the first to develop tools for estimating the dimension of parameters among distributions in exponential family and consequently,introduce the BIC to serve as an approximation to the Bayesian posterior probability of a given model.展开更多
The two-parameter Waring is an important heavy-tailed discrete distribution,which extends the famous Yule Simon distribution and provides more flexibility when modelling the data.The commonly used EFF(Expectation-Firs...The two-parameter Waring is an important heavy-tailed discrete distribution,which extends the famous Yule Simon distribution and provides more flexibility when modelling the data.The commonly used EFF(Expectation-First Frequency)for parameter estimation can only be applied when the first moment exists,and it only uses the information of the expectation and the first frequency,which is not as efficient as the maximum likelihood estimator(MLE).However,the MLE may not exist for some sample data.We apply the profle method to the log-likelihood function and derive the necessary and sufficient Conditions for the existence of the MLE of the Waring parameters.We use extensive simulation studies to compare the MLE and EFF methods,and the goodness-of-fit comparison with the Yule Simon distribution.We also apply the Waring distribution to fit an insurance data.展开更多
With the development of modern science and technology, more and more high-dimensionaldata appear in the application fields. Since the high dimension can potentially increase the com-plexity of the covariance structure...With the development of modern science and technology, more and more high-dimensionaldata appear in the application fields. Since the high dimension can potentially increase the com-plexity of the covariance structure, comparing the covariance matrices among populations isstrongly motivated in high-dimensional data analysis. In this article, we consider the proportion-ality test of two high-dimensional covariance matrices, where the data dimension is potentiallymuch larger than the sample sizes, or even larger than the squares of the sample sizes. We devisea novel high-dimensional spatial rank test that has much-improved power than many exist-ing popular tests, especially for the data generated from some heavy-tailed distributions. Theasymptotic normality of the proposed test statistics is established under the family of ellipticallysymmetric distributions, which is a more general distribution family than the normal distribu-tion family, including numerous commonly used heavy-tailed distributions. Extensive numericalexperiments demonstrate the superiority of the proposed test in terms of both empirical sizeand power. Then, a real data analysis demonstrates the practicability of the proposed test forhigh-dimensional gene expression data.展开更多
Due tocost effectiveness and hIgh efidengy.two-phase Qse control sampling has been wldely used In epldemlology studles.We dewelop a seml-parametric empinial lkellood approach to two-phase ase-control data under the lo...Due tocost effectiveness and hIgh efidengy.two-phase Qse control sampling has been wldely used In epldemlology studles.We dewelop a seml-parametric empinial lkellood approach to two-phase ase-control data under the logst regresslon model.we show that the maxmum empintal lklhoo estimaton has an aymptotically nomal dstibutlon,n,and the empincal lke-lthood ratlo fllws an aymptotcallycentral chi-square dstibution We find that the maxdmum empintial lkellhood estimator Is equal to Breslow and Holubkow(1997175 madimum lkelhood estimator.Evenso,the lmting dstribution of the lkelhood ratio,helhlodratlo based interval,and test are all new.Futhemmiore,we construct new Kolmogorov-smimnov type godnes-F-fit tests to test the vlldation of the undertying lglstic rgressonmodelLour simulation results and a real pplcaion show that the lola based Interval and test hawe certain mentsowver the wald-type counterparts and that the proposed godness-f-f test Is vald.展开更多
Semiparametric mixed-effects double regression models have been used for analysis of longitu-dinal data in a variety of applications,as they allow researchers to jointly model the mean and variance of the mixed-effect...Semiparametric mixed-effects double regression models have been used for analysis of longitu-dinal data in a variety of applications,as they allow researchers to jointly model the mean and variance of the mixed-effects as a function of predictors.However,these models are commonly estimated based on the normality assumption for the errors and the results may thus be sensitive to outliers and/or heavy-tailed data.Quantile regression is an ideal alternative to deal with these problems,as it is insensitive to heteroscedasticity and outliers and can make statistical analysis more robust.In this paper,we consider Bayesian quantile regression analysis for semiparamet-ric mixed-effects double regression models based on the asymmetric Laplace distribution for the errors.We construct a Bayesian hierarchical model and then develop an efficient Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full posterior dis-tributions to conduct the posterior inference.The performance of the proposed procedure is evaluated through simulation studies and a real data application.展开更多
Orthogonal matching pursuit(OMP)algorithm is a classical greedy algorithm widely used in compressed sensing.In this paper,by exploiting the Wielandt inequality and some properties of orthogonal projection matrix,we ob...Orthogonal matching pursuit(OMP)algorithm is a classical greedy algorithm widely used in compressed sensing.In this paper,by exploiting the Wielandt inequality and some properties of orthogonal projection matrix,we obtained a new number of iterations required for the OMP algorithm to perform exact recovery of sparse signals,which improves significantly upon the latest results as we know.展开更多
The academic community should be indebted to Professors Jun Cai and Yichun Chi for their meticulously written review paper(referred to as Cai&Chi,in press in what follows)on optimal reinsurance,which summarises an...The academic community should be indebted to Professors Jun Cai and Yichun Chi for their meticulously written review paper(referred to as Cai&Chi,in press in what follows)on optimal reinsurance,which summarises and synthesises the historical developments and recent advances in this burgeoning research field.展开更多
In this paper, we proposed a dynamic stress–strength model for coherent system. It is supposedthat the system consists of n components with initial random strength and each component issubjected to random stresses. T...In this paper, we proposed a dynamic stress–strength model for coherent system. It is supposedthat the system consists of n components with initial random strength and each component issubjected to random stresses. The stresses, applied repeatedly at random cycle times, will causethe degradation of strength. In addition, the number of cycles in an interval is assumed to followa Poisson distribution. In the case of the strength and stress random variables following exponential distributions, the expression for the reliability of the proposed dynamic stress–strengthmodel is derived based on survival signature. The reliability is estimated by using the best linearunbiased estimation (BLUE). Considering the Type-II censored failure times, the best linear unbiased predictors (BLUP) for the unobserved coherent system failure times are developed basedon the observed failure times. Monte Carlo simulations are performed to compare the BLUE ofparameters with different values and compute the BLUP. A real data set is also analysed for anillustration of the findings.展开更多
This speech was delivered at the Banquet and Award Ceremony June 17, 2018, during SAE 2018– an international conference on ‘Small Area Estimation and Other Topics of Current Interest inSurveys, Official Statistics, ...This speech was delivered at the Banquet and Award Ceremony June 17, 2018, during SAE 2018– an international conference on ‘Small Area Estimation and Other Topics of Current Interest inSurveys, Official Statistics, and General Statistics: A Celebration of Professor Danny Pfeffermann’s75th Birthday.展开更多
Treatment selection based on patient characteristics has been widely recognised in modern medicine.In this paper,we propose a generalised partially linear single-index mixed-effects modelling strategy for treatment se...Treatment selection based on patient characteristics has been widely recognised in modern medicine.In this paper,we propose a generalised partially linear single-index mixed-effects modelling strategy for treatment selection and heterogeneous treatment effect estimation in longitudinal clinical and observational studies.We model the treatment effect as an unknown functional curve of a weighted linear combination of time-dependent covariates.This method enables us to investigate covariate-specific treatment effects and make personalised treatment selection in a flexible fashion.We develop a method that combines local linear regression and penalised quasi-likelihood to estimate the weight for each covariate,the unknown treatment effect curve and the parameters for mixed-effects.Based on pointwise confidence intervals for the treatment effect curve,we can make individualised treatment decisions from the information of patient characteristics.A simulation study is conducted to evaluate finite sample performance of the proposed method.We also illustrate the method via analysis of a real data example.展开更多
It iswell known that traditionalmean-variance optimal portfolio delivers rather erratic and unsatisfactory out-of-sample performance due to the neglect of estimation errors.Constrained solutions,such as no-short-sale-...It iswell known that traditionalmean-variance optimal portfolio delivers rather erratic and unsatisfactory out-of-sample performance due to the neglect of estimation errors.Constrained solutions,such as no-short-sale-constrained and norm-constrained portfolios,can usually achieve much higher ex post Sharpe ratio.Bayesian methods have also been shown to be superior to traditional plug-in estimator by incorporating parameter uncertainty through prior distributions.In this paper,we develop an innovative method that induces priors directly on optimal portfolio weights and imposing constraints a priori in our hierarchical Bayes model.We showthat such constructed portfolios are well diversified with superior out-of-sample performance.Our proposed model is tested on a number of Fama–French industry portfolios against the na飗e diversification strategy and Chevrier and McCulloch’s(2008)economically motivated prior(EMP)strategy.On average,our model outperforms Chevrier and McCulloch’s(2008)EMP strategy by over 15%and outperform the‘1/N’strategy by over 50%.展开更多
Smoothing spline is a popular method in non-parametric function estimation.For the analysis of data from real applications,specific shapes on the estimated function are often required to ensure the estimated function ...Smoothing spline is a popular method in non-parametric function estimation.For the analysis of data from real applications,specific shapes on the estimated function are often required to ensure the estimated function undeviating from the domain knowledge.In this work,we focus on constructing the exact shape constrained smoothing spline with efficient estimation.The‘exact’here is referred as to impose the shape constraint on an infinite set such as an interval in one-dimensional case.Thus the estimation becomes a so-called semi-infinite optimisation problem with an infinite number of constraints.The proposed method is able to establish a sufficient and necessary condition for transforming the exact shape constraints to a finite number of constraints,leading to efficient estimation of the shape constrained functions.The performance of the proposed methods is evaluated by both simulation and real case studies.展开更多
We present a new approach to model selection and Bayes factor determination,based on Laplaceexpansions(as in BIC),which we call Prior-based Bayes Information Criterion(PBIC).In thisapproach,the Laplace expansion is on...We present a new approach to model selection and Bayes factor determination,based on Laplaceexpansions(as in BIC),which we call Prior-based Bayes Information Criterion(PBIC).In thisapproach,the Laplace expansion is only done with the likelihood function,and then a suitableprior distribution is chosen to allow exact computation of the(approximate)marginal likelihoodarising from the Laplace approximation and the prior.The result is a closed-form expression similar to BIC,but now involves a term arising from the prior distribution(which BIC ignores)andalso incorporates the idea that different parameters can have different effective sample sizes(whereas BIC only allows one overall sample size n).We also consider a modification of PBIC whichis more favourable to complex models.展开更多
The intraclass correlation coefficient (ICC) plays an important role in various fields of study asa coefficient of reliability. In this paper, we consider objective Bayesian analysis for the ICCin the context of norma...The intraclass correlation coefficient (ICC) plays an important role in various fields of study asa coefficient of reliability. In this paper, we consider objective Bayesian analysis for the ICCin the context of normal linear regression model. We first derive two objective priors for theunknown parameters and show that both result in proper posterior distributions. Within aBayesian decision-theoretic framework, we then propose an objective Bayesian solution to theproblems of hypothesis testing and point estimation of the ICC based on a combined use of theintrinsic discrepancy loss function and objective priors. The proposed solution has an appealinginvariance property under one-to-one reparametrisation of the quantity of interest. Simulationstudies are conducted to investigate the performance the proposed solution. Finally, a real dataapplication is provided for illustrative purposes.展开更多
Several fields,such as biological,medical,public health,agricultural sciences,etc.,require circular balanced repeated measurement designs with fewer unequal number of repeated measure-ments than the number of treatmen...Several fields,such as biological,medical,public health,agricultural sciences,etc.,require circular balanced repeated measurement designs with fewer unequal number of repeated measure-ments than the number of treatments.Also,the availability and high cost of experimental subjects in these fields prefer the design in fewer experimental units.However,balancing the carryover effects of the treatments in minimal experimental subjects is one of the problems in this case.In this paper,several new series of minimal circular nearly strongly balanced RMDs in periods of two and three different sizes are constructed.The proposed construction of designs has high efficiency and,therefore,can save the cost of experimentations due to a fewer exper-imental subjects.Most of the designs are very useful because of the unavailability of strongly balanced RMDs for these combinations of parameters.A list of sets of shifts for the construction of minimal circular nearly SBRMDs has also been mentioned in the Appendix.展开更多
Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this paper.Similar to empirical lik...Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this paper.Similar to empirical likelihood(EL),it still suffers from two drawbacks:the nondefinition problem of the likelihood function and the under-coverage probability of confidence region.To overcome these two problems,we further proposed the adjusted ET(AET)likelihood.With a specific adjustment level,our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method.In addition,due to the good performance of ET under moment model misspecification[Schennach,S.M.(2007).Point estimation with exponentially tilted empirical likelihood.The Annals of Statistics,35(2),634–672.https://doi.org/10.1214/009053606000001208],we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1).The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation.A real data set is analyzed for illustration purpose.展开更多
A good visualisation method can greatly enhance human-machine collaboration in target contexts.To aid the optimal selection of visualisations for users,visualisation recommender systems have been developed to provide ...A good visualisation method can greatly enhance human-machine collaboration in target contexts.To aid the optimal selection of visualisations for users,visualisation recommender systems have been developed to provide the right visualisation method to the right person given specific contexts.A visualisation recommender system often relies on a user study to collect data and conduct analysis to provide personalised recommendations.However,a user study without employing an effective experimental design is typically expensive in terms of time and cost.In this work,we propose a prediction-oriented optimal design to determine the user-task allocation in the user study for the recommendation of visualisation methods.The proposed optimal design will not only encourage the learning of the similarity embedded in the recommendation responses(i.e.,users’preference),but also improve the modelling accuracy of the similarities captured by the covariates of contexts(i.e.,task attributes).A simulation study and a real-data case study are used to evaluate the proposed optimal design.展开更多
In a repairable consecutive C(k,n:F)system,after the system operates for a certain time,some components may fail,some failed components may be repaired and the state of the system may change.The models developed in th...In a repairable consecutive C(k,n:F)system,after the system operates for a certain time,some components may fail,some failed components may be repaired and the state of the system may change.The models developed in the existing literature usually assume that the state of the sys-tem varies over time depending on the values of n and k and the state of the system is known.Since the system reliability will vary over time,it is of great interest to analyse the time-dependent system reliability.In this paper,we develop a novel and simple method that utilizes the eigen-values of the transition rate matrix of the system for the computation of time-dependent system reliability when the system state is known.In addition,the transition performance probabilities of the system from a known state to the possible states are also analysed.Computational results are presented to illustrate the applicability and accuracy of the proposed method.展开更多
基金the Fundamental Research Funds for the Central Universities of China(No.2232020D-43).
文摘This paper studies the inference problem of index coefficient in single-index models under massive dataset.Analysis of massive dataset is challenging owing to formidable computational costs or memory requirements.A natural method is the averaging divide-and-conquer approach,which splits data into several blocks,obtains the estimators for each block and then aggregates the estimators via averaging.However,there is a restriction on the number of blocks.To overcome this limitation,this paper proposed a computationally efficient method,which only requires an initial estimator and then successively refines the estimator via multiple rounds of aggregations.The proposed estimator achieves the optimal convergence rate without any restriction on the number of blocks.We present both theoretical analysis and experiments to explore the property of the proposed method.
文摘Many of the best predictors for complex problems are typically regarded as hard to interpret physically.These include kernel methods,Shtarkov solutions,and random forests.We show that,despite the inability to interpret these three predictors to infinite precision,they can be asymptotically approximated and admit conceptual interpretations in terms of their mathe-matical/statistical properties.The resulting expressions can be in terms of polynomials,basis elements,or other functions that an analyst may regard as interpretable.
基金This work was supported by the Natural Sciences and Engineering Research Council of Canada[566065 and 587391].
文摘We would like to thank the authors(Bayarri et al.,2018)for their interesting and provoking paper,and we wish to discuss some issues related to sample size in general and the number of covariates in the context of linear regression model when using the Bayesian information criteria(BIC)for model selection.Schwarz(1978)was the first to develop tools for estimating the dimension of parameters among distributions in exponential family and consequently,introduce the BIC to serve as an approximation to the Bayesian posterior probability of a given model.
基金This work is partially supported by National Natural Science Foundation of China[Grant Numbers 11671096,11690013,11731011,11871376]Natural Science Foundation of Shanghai[Grant Number 21ZR1420700].
文摘The two-parameter Waring is an important heavy-tailed discrete distribution,which extends the famous Yule Simon distribution and provides more flexibility when modelling the data.The commonly used EFF(Expectation-First Frequency)for parameter estimation can only be applied when the first moment exists,and it only uses the information of the expectation and the first frequency,which is not as efficient as the maximum likelihood estimator(MLE).However,the MLE may not exist for some sample data.We apply the profle method to the log-likelihood function and derive the necessary and sufficient Conditions for the existence of the MLE of the Waring parameters.We use extensive simulation studies to compare the MLE and EFF methods,and the goodness-of-fit comparison with the Yule Simon distribution.We also apply the Waring distribution to fit an insurance data.
基金This work was supported by the National Natural Sci-ence Foundation of China[Grant Numbers 11501092,11571068]the Special Fund for Key Laboratories of Jilin Province,China[Grant Number 20190201285JC].
文摘With the development of modern science and technology, more and more high-dimensionaldata appear in the application fields. Since the high dimension can potentially increase the com-plexity of the covariance structure, comparing the covariance matrices among populations isstrongly motivated in high-dimensional data analysis. In this article, we consider the proportion-ality test of two high-dimensional covariance matrices, where the data dimension is potentiallymuch larger than the sample sizes, or even larger than the squares of the sample sizes. We devisea novel high-dimensional spatial rank test that has much-improved power than many exist-ing popular tests, especially for the data generated from some heavy-tailed distributions. Theasymptotic normality of the proposed test statistics is established under the family of ellipticallysymmetric distributions, which is a more general distribution family than the normal distribu-tion family, including numerous commonly used heavy-tailed distributions. Extensive numericalexperiments demonstrate the superiority of the proposed test in terms of both empirical sizeand power. Then, a real data analysis demonstrates the practicability of the proposed test forhigh-dimensional gene expression data.
基金The research was supported by theNationalNatural Science Foundation of China[grant number 11771144]the State Key Program of National Natural Science Foundation of China[grant number 71931004],[grant number 32030063]the development fund for Shanghai talents,and the 111 project(B14019).
文摘Due tocost effectiveness and hIgh efidengy.two-phase Qse control sampling has been wldely used In epldemlology studles.We dewelop a seml-parametric empinial lkellood approach to two-phase ase-control data under the logst regresslon model.we show that the maxmum empintal lklhoo estimaton has an aymptotically nomal dstibutlon,n,and the empincal lke-lthood ratlo fllws an aymptotcallycentral chi-square dstibution We find that the maxdmum empintial lkellhood estimator Is equal to Breslow and Holubkow(1997175 madimum lkelhood estimator.Evenso,the lmting dstribution of the lkelhood ratio,helhlodratlo based interval,and test are all new.Futhemmiore,we construct new Kolmogorov-smimnov type godnes-F-fit tests to test the vlldation of the undertying lglstic rgressonmodelLour simulation results and a real pplcaion show that the lola based Interval and test hawe certain mentsowver the wald-type counterparts and that the proposed godness-f-f test Is vald.
基金Dr.Wu was supported by the National Natural Science Foundation of China under grant 11861041Drs.Keying Ye and Min Wang were partially supported by a grant from the UTSA Vice President for Research,Economic Development,and Knowledge Enterprise at the University of Texas at San Antonio.
文摘Semiparametric mixed-effects double regression models have been used for analysis of longitu-dinal data in a variety of applications,as they allow researchers to jointly model the mean and variance of the mixed-effects as a function of predictors.However,these models are commonly estimated based on the normality assumption for the errors and the results may thus be sensitive to outliers and/or heavy-tailed data.Quantile regression is an ideal alternative to deal with these problems,as it is insensitive to heteroscedasticity and outliers and can make statistical analysis more robust.In this paper,we consider Bayesian quantile regression analysis for semiparamet-ric mixed-effects double regression models based on the asymmetric Laplace distribution for the errors.We construct a Bayesian hierarchical model and then develop an efficient Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full posterior dis-tributions to conduct the posterior inference.The performance of the proposed procedure is evaluated through simulation studies and a real data application.
基金support from the National Natural Science Foundation of China No.11971204Natural Science Foundation of Jiangsu Province of China No.BK20200108the Zhongwu Youth Innovative Talent Program of Jiangsu University of Technology.
文摘Orthogonal matching pursuit(OMP)algorithm is a classical greedy algorithm widely used in compressed sensing.In this paper,by exploiting the Wielandt inequality and some properties of orthogonal projection matrix,we obtained a new number of iterations required for the OMP algorithm to perform exact recovery of sparse signals,which improves significantly upon the latest results as we know.
基金Support from a Centers of Actuarial Excellence(CAE)Research Grant(2018-2021)from the Society of Actuaries.
文摘The academic community should be indebted to Professors Jun Cai and Yichun Chi for their meticulously written review paper(referred to as Cai&Chi,in press in what follows)on optimal reinsurance,which summarises and synthesises the historical developments and recent advances in this burgeoning research field.
基金This work is supported by the National Natural Science Foundation of China[71571144,71401134,71171164,11701406]The Natural Science Basic Research Program of Shaanxi Province[2015JM1003]The Program of international Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province[2016KW-033].
文摘In this paper, we proposed a dynamic stress–strength model for coherent system. It is supposedthat the system consists of n components with initial random strength and each component issubjected to random stresses. The stresses, applied repeatedly at random cycle times, will causethe degradation of strength. In addition, the number of cycles in an interval is assumed to followa Poisson distribution. In the case of the strength and stress random variables following exponential distributions, the expression for the reliability of the proposed dynamic stress–strengthmodel is derived based on survival signature. The reliability is estimated by using the best linearunbiased estimation (BLUE). Considering the Type-II censored failure times, the best linear unbiased predictors (BLUP) for the unobserved coherent system failure times are developed basedon the observed failure times. Monte Carlo simulations are performed to compare the BLUE ofparameters with different values and compute the BLUP. A real data set is also analysed for anillustration of the findings.
文摘This speech was delivered at the Banquet and Award Ceremony June 17, 2018, during SAE 2018– an international conference on ‘Small Area Estimation and Other Topics of Current Interest inSurveys, Official Statistics, and General Statistics: A Celebration of Professor Danny Pfeffermann’s75th Birthday.
基金supported by Natural Science Foundation of Shanghai(17ZR1409000)funded by NIA/NIH Grant U01 AG016976.
文摘Treatment selection based on patient characteristics has been widely recognised in modern medicine.In this paper,we propose a generalised partially linear single-index mixed-effects modelling strategy for treatment selection and heterogeneous treatment effect estimation in longitudinal clinical and observational studies.We model the treatment effect as an unknown functional curve of a weighted linear combination of time-dependent covariates.This method enables us to investigate covariate-specific treatment effects and make personalised treatment selection in a flexible fashion.We develop a method that combines local linear regression and penalised quasi-likelihood to estimate the weight for each covariate,the unknown treatment effect curve and the parameters for mixed-effects.Based on pointwise confidence intervals for the treatment effect curve,we can make individualised treatment decisions from the information of patient characteristics.A simulation study is conducted to evaluate finite sample performance of the proposed method.We also illustrate the method via analysis of a real data example.
基金This work was supported in part by US National Science Foundation(NSF)under grant DMS-1613110。
文摘It iswell known that traditionalmean-variance optimal portfolio delivers rather erratic and unsatisfactory out-of-sample performance due to the neglect of estimation errors.Constrained solutions,such as no-short-sale-constrained and norm-constrained portfolios,can usually achieve much higher ex post Sharpe ratio.Bayesian methods have also been shown to be superior to traditional plug-in estimator by incorporating parameter uncertainty through prior distributions.In this paper,we develop an innovative method that induces priors directly on optimal portfolio weights and imposing constraints a priori in our hierarchical Bayes model.We showthat such constructed portfolios are well diversified with superior out-of-sample performance.Our proposed model is tested on a number of Fama–French industry portfolios against the na飗e diversification strategy and Chevrier and McCulloch’s(2008)economically motivated prior(EMP)strategy.On average,our model outperforms Chevrier and McCulloch’s(2008)EMP strategy by over 15%and outperform the‘1/N’strategy by over 50%.
基金supported by National Science Foundation[1634867].
文摘Smoothing spline is a popular method in non-parametric function estimation.For the analysis of data from real applications,specific shapes on the estimated function are often required to ensure the estimated function undeviating from the domain knowledge.In this work,we focus on constructing the exact shape constrained smoothing spline with efficient estimation.The‘exact’here is referred as to impose the shape constraint on an infinite set such as an interval in one-dimensional case.Thus the estimation becomes a so-called semi-infinite optimisation problem with an infinite number of constraints.The proposed method is able to establish a sufficient and necessary condition for transforming the exact shape constraints to a finite number of constraints,leading to efficient estimation of the shape constrained functions.The performance of the proposed methods is evaluated by both simulation and real case studies.
基金M.J.Bayarri’s research was supported by the Spanish Ministry of Education and Science[grant number MTM2010-19528]James Berger’s research was supported by USA National Science Foundation[grant numbers DMS-1007773 and DMS-1407775]+1 种基金Woncheol Jang’s research was supported by the National Research Foundation of Korea(NRF)grants funded by the Korea government(MSIP),No.2014R1A4A1007895 and No.2017R1A2B2012816Luis Pericchi’s research was supported by grant CA096297/CA096300 from the USA National Cancer Institute of the National Institutes of Health.
文摘We present a new approach to model selection and Bayes factor determination,based on Laplaceexpansions(as in BIC),which we call Prior-based Bayes Information Criterion(PBIC).In thisapproach,the Laplace expansion is only done with the likelihood function,and then a suitableprior distribution is chosen to allow exact computation of the(approximate)marginal likelihoodarising from the Laplace approximation and the prior.The result is a closed-form expression similar to BIC,but now involves a term arising from the prior distribution(which BIC ignores)andalso incorporates the idea that different parameters can have different effective sample sizes(whereas BIC only allows one overall sample size n).We also consider a modification of PBIC whichis more favourable to complex models.
文摘The intraclass correlation coefficient (ICC) plays an important role in various fields of study asa coefficient of reliability. In this paper, we consider objective Bayesian analysis for the ICCin the context of normal linear regression model. We first derive two objective priors for theunknown parameters and show that both result in proper posterior distributions. Within aBayesian decision-theoretic framework, we then propose an objective Bayesian solution to theproblems of hypothesis testing and point estimation of the ICC based on a combined use of theintrinsic discrepancy loss function and objective priors. The proposed solution has an appealinginvariance property under one-to-one reparametrisation of the quantity of interest. Simulationstudies are conducted to investigate the performance the proposed solution. Finally, a real dataapplication is provided for illustrative purposes.
文摘Several fields,such as biological,medical,public health,agricultural sciences,etc.,require circular balanced repeated measurement designs with fewer unequal number of repeated measure-ments than the number of treatments.Also,the availability and high cost of experimental subjects in these fields prefer the design in fewer experimental units.However,balancing the carryover effects of the treatments in minimal experimental subjects is one of the problems in this case.In this paper,several new series of minimal circular nearly strongly balanced RMDs in periods of two and three different sizes are constructed.The proposed construction of designs has high efficiency and,therefore,can save the cost of experimentations due to a fewer exper-imental subjects.Most of the designs are very useful because of the unavailability of strongly balanced RMDs for these combinations of parameters.A list of sets of shifts for the construction of minimal circular nearly SBRMDs has also been mentioned in the Appendix.
基金supported by Natural Science Foundation of Shanghai(17ZR1409000)National Natural Science Foundation of China(11831008,11971171)the Open Research Fundof KeyLaboratory of Advanced Theory andApplication in Statistics and Data Science-MOE,ECNU.
文摘Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this paper.Similar to empirical likelihood(EL),it still suffers from two drawbacks:the nondefinition problem of the likelihood function and the under-coverage probability of confidence region.To overcome these two problems,we further proposed the adjusted ET(AET)likelihood.With a specific adjustment level,our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method.In addition,due to the good performance of ET under moment model misspecification[Schennach,S.M.(2007).Point estimation with exponentially tilted empirical likelihood.The Annals of Statistics,35(2),634–672.https://doi.org/10.1214/009053606000001208],we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1).The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation.A real data set is analyzed for illustration purpose.
文摘A good visualisation method can greatly enhance human-machine collaboration in target contexts.To aid the optimal selection of visualisations for users,visualisation recommender systems have been developed to provide the right visualisation method to the right person given specific contexts.A visualisation recommender system often relies on a user study to collect data and conduct analysis to provide personalised recommendations.However,a user study without employing an effective experimental design is typically expensive in terms of time and cost.In this work,we propose a prediction-oriented optimal design to determine the user-task allocation in the user study for the recommendation of visualisation methods.The proposed optimal design will not only encourage the learning of the similarity embedded in the recommendation responses(i.e.,users’preference),but also improve the modelling accuracy of the similarities captured by the covariates of contexts(i.e.,task attributes).A simulation study and a real-data case study are used to evaluate the proposed optimal design.
基金H.K.T.Ng’s work was also supported by a grant from the Simons Foundation[Grant Number 709773]。
文摘In a repairable consecutive C(k,n:F)system,after the system operates for a certain time,some components may fail,some failed components may be repaired and the state of the system may change.The models developed in the existing literature usually assume that the state of the sys-tem varies over time depending on the values of n and k and the state of the system is known.Since the system reliability will vary over time,it is of great interest to analyse the time-dependent system reliability.In this paper,we develop a novel and simple method that utilizes the eigen-values of the transition rate matrix of the system for the computation of time-dependent system reliability when the system state is known.In addition,the transition performance probabilities of the system from a known state to the possible states are also analysed.Computational results are presented to illustrate the applicability and accuracy of the proposed method.
