This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectatio...This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model.The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis,and tends to infinity in probability under the alternative hypothesis,which implies the consistency of the test.Furthermore,it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis.Extensive simulations are reported,and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies.The proposed methods are also applied to two real datasets.展开更多
In this paper,the authors propose a frequentist model averaging method for composite quantile regression with diverging number of parameters.Different from the traditional model averaging for quantile regression which...In this paper,the authors propose a frequentist model averaging method for composite quantile regression with diverging number of parameters.Different from the traditional model averaging for quantile regression which considers only a single quantile,the proposed model averaging estimator is based on multiple quantiles.The well-known delete-one cross-validation or jackknife approach is applied to estimate the model weights.The resultant jackknife model averaging estimator is shown to be asymptotically optimal in terms of minimizing the out-of-sample composite final prediction error.Simulation studies are conducted to demonstrate the finite sample performance of the new model averaging estimator.The proposed method is also applied to the analysis of the stock returns data and the wage data.展开更多
We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH mo...We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator.The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions.The proposed methodology is also illustrated by Va R on stock price data.展开更多
In this paper,we consider composite quantile regression for partial functional linear regression model with polynomial spline approximation.Under some mild conditions,the convergence rates of the estimators and mean s...In this paper,we consider composite quantile regression for partial functional linear regression model with polynomial spline approximation.Under some mild conditions,the convergence rates of the estimators and mean squared prediction error,and asymptotic normality of parameter vector are obtained.Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least-squares based method when there are outliers in the dataset or the random error follows heavy-tailed distributions.Finally,we apply the proposed methodology to a spectroscopic data sets to illustrate its usefulness in practice.展开更多
Recently, variable selection based on penalized regression methods has received a great deal of attention, mostly through frequentist＇s models. This paper investigates regularization regression from Bayesian perspect...Recently, variable selection based on penalized regression methods has received a great deal of attention, mostly through frequentist＇s models. This paper investigates regularization regression from Bayesian perspective. Our new method extends the Bayesian Lasso regression （Park and Casella, 2008） through replacing the least square loss and Lasso penalty by composite quantile loss function and adaptive Lasso penalty, which allows different penalization parameters for different regression coefficients. Based on the Bayesian hierarchical model framework, an efficient Gibbs sampler is derived to simulate the parameters from posterior distributions. Furthermore, we study the Bayesian composite quantile regression with adaptive group Lasso penalty. The distinguishing characteristic of the newly proposed method is completely data adaptive without requiring prior knowledge of the error distribution. Extensive simulations and two real data examples are used to examine the good performance of the proposed method. All results confirm that our novel method has both robustness and high efficiency and often outperforms other approaches.展开更多
Multilevel （hierarchical） modeling is a generalization of linear and generalized linear modeling in which regression coefficients are modeled through a model, whose parameters are also estimated from data. Multileve...Multilevel （hierarchical） modeling is a generalization of linear and generalized linear modeling in which regression coefficients are modeled through a model, whose parameters are also estimated from data. Multilevel model fails to fit well typically by the use of the EM algorithm once one of level error variance （like Cauchy distribution） tends to infinity. This paper proposes a composite multilevel to combine the nested structure of multilevel data and the robustness of the composite quantile regression, which greatly improves the efficiency and precision of the estimation. The new approach, which is based on the Gauss-Seidel iteration and takes a full advantage of the composite quantile regression and multilevel models, still works well when the error variance tends to infinity, We show that even the error distribution is normal, the MSE of the estimation of composite multilevel quantile regression models nearly equals to mean regression. When the error distribution is not normal, our method still enjoys great advantages in terms of estimation efficiency.展开更多
Based on the data-cutoff method,we study quantile regression in linear models,where the noise process is of Ornstein-Uhlenbeck type with possible jumps.In single-level quantile regression,we allow the noise process to...Based on the data-cutoff method,we study quantile regression in linear models,where the noise process is of Ornstein-Uhlenbeck type with possible jumps.In single-level quantile regression,we allow the noise process to be heteroscedastic,while in composite quantile regression,we require that the noise process be homoscedastic so that the slopes are invariant across quantiles.Similar to the independent noise case,the proposed quantile estimators are root-n consistent and asymptotic normal.Furthermore,the adaptive least absolute shrinkage and selection operator(LASSO)is applied for the purpose of variable selection.As a result,the quantile estimators are consistent in variable selection,and the nonzero coefficient estimators enjoy the same asymptotic distribution as their counterparts under the true model.Extensive numerical simulations are conducted to evaluate the performance of the proposed approaches and foreign exchange rate data are analyzed for the illustration purpose.展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.11271014 and 11971045。
文摘This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model.The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis,and tends to infinity in probability under the alternative hypothesis,which implies the consistency of the test.Furthermore,it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis.Extensive simulations are reported,and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies.The proposed methods are also applied to two real datasets.
基金supported by the National Natural Science Foundation of China under Grant Nos.11971323 and 12031016。
文摘In this paper,the authors propose a frequentist model averaging method for composite quantile regression with diverging number of parameters.Different from the traditional model averaging for quantile regression which considers only a single quantile,the proposed model averaging estimator is based on multiple quantiles.The well-known delete-one cross-validation or jackknife approach is applied to estimate the model weights.The resultant jackknife model averaging estimator is shown to be asymptotically optimal in terms of minimizing the out-of-sample composite final prediction error.Simulation studies are conducted to demonstrate the finite sample performance of the new model averaging estimator.The proposed method is also applied to the analysis of the stock returns data and the wage data.
基金supported by National Natural Science Foundation of China(Grant No.11371354)Key Laboratory of Random Complex Structures and Data Science+2 种基金Chinese Academy of Sciences(Grant No.2008DP173182)National Center for Mathematics and Interdisciplinary SciencesChinese Academy of Sciences
文摘We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator.The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions.The proposed methodology is also illustrated by Va R on stock price data.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671096,11690013,11731011 and 12071267)the Natural Science Foundation of Shanxi Province,China(Grant No.201901D111279)。
文摘In this paper,we consider composite quantile regression for partial functional linear regression model with polynomial spline approximation.Under some mild conditions,the convergence rates of the estimators and mean squared prediction error,and asymptotic normality of parameter vector are obtained.Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least-squares based method when there are outliers in the dataset or the random error follows heavy-tailed distributions.Finally,we apply the proposed methodology to a spectroscopic data sets to illustrate its usefulness in practice.
基金supported in part by National Natural Science Foundation of China(11501372,11571112)Project of National Social Science Fund(15BTJ027)+3 种基金Doctoral Fund of Ministry of Education of China(20130076110004)Program of Shanghai Subject Chief Scientist(14XD1401600)the 111 Project of China(B14019)Natural Science Fund of Nantong University(14B28)
文摘Recently, variable selection based on penalized regression methods has received a great deal of attention, mostly through frequentist＇s models. This paper investigates regularization regression from Bayesian perspective. Our new method extends the Bayesian Lasso regression （Park and Casella, 2008） through replacing the least square loss and Lasso penalty by composite quantile loss function and adaptive Lasso penalty, which allows different penalization parameters for different regression coefficients. Based on the Bayesian hierarchical model framework, an efficient Gibbs sampler is derived to simulate the parameters from posterior distributions. Furthermore, we study the Bayesian composite quantile regression with adaptive group Lasso penalty. The distinguishing characteristic of the newly proposed method is completely data adaptive without requiring prior knowledge of the error distribution. Extensive simulations and two real data examples are used to examine the good performance of the proposed method. All results confirm that our novel method has both robustness and high efficiency and often outperforms other approaches.
基金The work was partially supported by Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(No.10XNL018)
文摘Multilevel （hierarchical） modeling is a generalization of linear and generalized linear modeling in which regression coefficients are modeled through a model, whose parameters are also estimated from data. Multilevel model fails to fit well typically by the use of the EM algorithm once one of level error variance （like Cauchy distribution） tends to infinity. This paper proposes a composite multilevel to combine the nested structure of multilevel data and the robustness of the composite quantile regression, which greatly improves the efficiency and precision of the estimation. The new approach, which is based on the Gauss-Seidel iteration and takes a full advantage of the composite quantile regression and multilevel models, still works well when the error variance tends to infinity, We show that even the error distribution is normal, the MSE of the estimation of composite multilevel quantile regression models nearly equals to mean regression. When the error distribution is not normal, our method still enjoys great advantages in terms of estimation efficiency.
基金supported by National Natural Science Foundation of China(Grant Nos.11801355 and 11971116).
文摘Based on the data-cutoff method,we study quantile regression in linear models,where the noise process is of Ornstein-Uhlenbeck type with possible jumps.In single-level quantile regression,we allow the noise process to be heteroscedastic,while in composite quantile regression,we require that the noise process be homoscedastic so that the slopes are invariant across quantiles.Similar to the independent noise case,the proposed quantile estimators are root-n consistent and asymptotic normal.Furthermore,the adaptive least absolute shrinkage and selection operator(LASSO)is applied for the purpose of variable selection.As a result,the quantile estimators are consistent in variable selection,and the nonzero coefficient estimators enjoy the same asymptotic distribution as their counterparts under the true model.Extensive numerical simulations are conducted to evaluate the performance of the proposed approaches and foreign exchange rate data are analyzed for the illustration purpose.
