Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that t...Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n-1/2). Finally, an example concerning the main result is given.展开更多
Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters.In this article,it is shown that for a nondecreasing u1(t),under some mild conditions the recursive M-e...Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters.In this article,it is shown that for a nondecreasing u1(t),under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed.Furthermore,optimal recursive M-estimators,asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.展开更多
Let {vij}, i, j = 1, 2,…, be i.i.d. random variables with Ev11= 0, Ev112=1 and ai = (ai1,…,aiM) be random vectors with {aij} being i.i.d. random variables. Define XN=(x1,…, XK) and SN= XNXNT, where The spectral dis...Let {vij}, i, j = 1, 2,…, be i.i.d. random variables with Ev11= 0, Ev112=1 and ai = (ai1,…,aiM) be random vectors with {aij} being i.i.d. random variables. Define XN=(x1,…, XK) and SN= XNXNT, where The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.展开更多
Consistency of LS estimate of simple linear EV model is studied. It is shown that under some common assumptions of the model, both weak and strong consistency of the estimate are equivalent but it is not so for quadra...Consistency of LS estimate of simple linear EV model is studied. It is shown that under some common assumptions of the model, both weak and strong consistency of the estimate are equivalent but it is not so for quadratic-mean consistency.展开更多
In this article,the empirical Bayes(EB)estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares(LS)...In this article,the empirical Bayes(EB)estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares(LS)estimator are investigated under mean square error matrix(MSEM)criterion.展开更多
In this paper, regression function estimation from independent and identically distributed data is considered. We establish strong pointwise consistency of the famous Nadaraya-Watson estimator under weaker conditions ...In this paper, regression function estimation from independent and identically distributed data is considered. We establish strong pointwise consistency of the famous Nadaraya-Watson estimator under weaker conditions which permit to apply kernels with unbounded support and even not integrable ones and provide a general approach for constructing strongly consistent kernel estimates of regression functions.展开更多
Based on the review of various methods of estimating Gini coefficient, the paper applies a quintile rule to estimate Gini coefficient of rural areas, urban areas and the whole country using the grouped income data of ...Based on the review of various methods of estimating Gini coefficient, the paper applies a quintile rule to estimate Gini coefficient of rural areas, urban areas and the whole country using the grouped income data of urban and rural residents. Besides, the paper uses the curve-fitting method to roughly estimate Gini coefficient from eye-catching Hurun Rich List and the latest poverty line. The result shows that the estimation of Gini coefficient using quintile rule is small for both urban and rural area, while the value of the whole country is obviously larger, which is above the warning line of 0.4. It is indicated that the wealth gap mainly comes from the gap between urban and rural areas. On the other hand, the estimation of Gini coefficient using curve-fitting method is as large as more than 0.7, which implies that the wealth gap is?highlighted from the analysis of the lowest and highest part of the wealth distribution. All in all, China’s current gap between the poor and the rich is serious. The reform of the income distribution needs to speed up to ensure social harmony and stability.展开更多
We study the quasi likelihood equation in Generalized Linear Models(GLM) with adaptive design ∑ni=1x_i(y_i-h(x_i′β))=0, where y_i is a q-vector, and x_i is a p×q random matrix. Under some assumptions, it is sh...We study the quasi likelihood equation in Generalized Linear Models(GLM) with adaptive design ∑ni=1x_i(y_i-h(x_i′β))=0, where y_i is a q-vector, and x_i is a p×q random matrix. Under some assumptions, it is shown that the Quasi-Likelihood equation for the GLM has a solution which is asymptotic normal.展开更多
Objective: To discover new proteomic biomarkers of hepatocellular carcinoma. Methods: Surface enhanced laser desorption/ionization time-of-flight (SELDI-TOF) mass spectrometry was used to discover biomarkers for diffe...Objective: To discover new proteomic biomarkers of hepatocellular carcinoma. Methods: Surface enhanced laser desorption/ionization time-of-flight (SELDI-TOF) mass spectrometry was used to discover biomarkers for differentiating hepatocellular carcinoma and chronic liver disease. A population of 50 patients with hepatocellular carcinoma and 33 patients with chronic liver disease was studied. Results: Twelve proteomic biomarkers of hepatocellular carcinoma were detected in this study. Three proteomic biomarkers were highly expressed in hepatocellular carcinoma and nine proteomic biomarkers were highly expressed in chronic liver disease. The most valuable proteomic biomarker with m/z=11498 had no similar diagnostic value as α-fetoprotein. Conclusion: Some of the twelve proteomic biomarkers may become new biomarkers of hepatocellular carcinoma.展开更多
For two independent non-negative random variables X and Y, we treat X as the initial variable of major importance and Y as a modifier (such as the interest rate of a portfolio).Stability in the tail behaviors of the p...For two independent non-negative random variables X and Y, we treat X as the initial variable of major importance and Y as a modifier (such as the interest rate of a portfolio).Stability in the tail behaviors of the product compared with that of the original variable X is of practical interests. In this paper, we study the tail behaviors of the product XY when the distribution of X belongs to the classes L and S, respectively. Under appropriate conditions, we show that the distribution of the product XY is in the same class as X when X belongs to class L or S, in other words, classes L and S are stable under some mild conditions on the distribution of Y. We also show that if the distribution of X is in class L(γ) (γ＞ 0) and continuous, then the product XY is in L if and only if Y is unbounded.展开更多
Under very weak condition 0 【 r(t)↑∞ , t→∞. we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for resear...Under very weak condition 0 【 r(t)↑∞ , t→∞. we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some results on strong law of large numbers are given such that our results are much stronger than the corresponding result of Gadidov’s.展开更多
Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of int...Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of interest rates becomes more important in pricing such long-dated options.In this paper,the pricing of Asian options under stochastic interest rates is studied.Assuming Hull and White model for the interest rates,a closed-form formula for geometric-average options is derived.As a by-product,pricing formula is also given for plan-vanilla options under stochastic interest rates.展开更多
For high-dimensional models with a focus on classification performance,the?1-penalized logistic regression is becoming important and popular.However,the Lasso estimates could be problematic when penalties of different...For high-dimensional models with a focus on classification performance,the?1-penalized logistic regression is becoming important and popular.However,the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data.We propose two types of weighted Lasso estimates,depending upon covariates determined by the Mc Diarmid inequality.Given sample size n and a dimension of covariates p,the finite sample behavior of our proposed method with a diverging number of predictors is illustrated by non-asymptotic oracle inequalities such as the?1-estimation error and the squared prediction error of the unknown parameters.We compare the performance of our method with that of former weighted estimates on simulated data,then apply it to do real data analysis.展开更多
In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is as...In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.展开更多
This paper investigates the pricing of options written on non-traded assets and trading strategies for the stock and option in an exponential utility maximization framework.Under the assumption that the option can be ...This paper investigates the pricing of options written on non-traded assets and trading strategies for the stock and option in an exponential utility maximization framework.Under the assumption that the option can be continuously traded without friction just as the stock,a dynamic relationship between their optimal positions is derived by using the stochastic dynamic programming techniques.The dynamic option pricing equations are also established.In particular,the properties of the associated solutions are discussed and their explicit representations are demonstrated via the Feynman-Kac formula.This paper further compares the dynamic option price to the existing price notions,such as the marginal price and indifference price.展开更多
The strong convergence and convergence rate of the random quadratic formss1T(S1S1T)ms1 and s1T(SST)ms1 are set up. The application of these results in wireless communication is given. Simulation results are presented.
In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the ...In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.展开更多
The changes of numeraire can be used as a very powerful tool in pricing contingent claims in the context of a complete market.By using the method of numeraire changes to evaluate convertible bonds when the value of fi...The changes of numeraire can be used as a very powerful tool in pricing contingent claims in the context of a complete market.By using the method of numeraire changes to evaluate convertible bonds when the value of firm,and those of zero-coupon bonds follow general adapted stochastic processes in this paper,using Ito theorem and Gisanov theorem.A closed-form solution is derived under the stochastic volatility by using fast Fourier transforms.展开更多
基金The project is partly supported by NSFC (19971085)the Doctoral Program Foundation of the Institute of High Education and the Special Foundation of Chinese Academy of Sciences.
文摘Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n-1/2). Finally, an example concerning the main result is given.
基金supported by the Natural Sciences and Engineering Research Council of Canadathe National Natural Science Foundation of China+2 种基金the Doctorial Fund of Education Ministry of Chinasupported by the Natural Sciences and Engineering Research Council of Canadasupported by the National Natural Science Foundation of China
文摘Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters.In this article,it is shown that for a nondecreasing u1(t),under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed.Furthermore,optimal recursive M-estimators,asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.
文摘Let {vij}, i, j = 1, 2,…, be i.i.d. random variables with Ev11= 0, Ev112=1 and ai = (ai1,…,aiM) be random vectors with {aij} being i.i.d. random variables. Define XN=(x1,…, XK) and SN= XNXNT, where The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.
文摘Consistency of LS estimate of simple linear EV model is studied. It is shown that under some common assumptions of the model, both weak and strong consistency of the estimate are equivalent but it is not so for quadratic-mean consistency.
基金the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX3-SYW-S02)the Youth Foundation of USTC
文摘In this article,the empirical Bayes(EB)estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares(LS)estimator are investigated under mean square error matrix(MSEM)criterion.
文摘In this paper, regression function estimation from independent and identically distributed data is considered. We establish strong pointwise consistency of the famous Nadaraya-Watson estimator under weaker conditions which permit to apply kernels with unbounded support and even not integrable ones and provide a general approach for constructing strongly consistent kernel estimates of regression functions.
文摘Based on the review of various methods of estimating Gini coefficient, the paper applies a quintile rule to estimate Gini coefficient of rural areas, urban areas and the whole country using the grouped income data of urban and rural residents. Besides, the paper uses the curve-fitting method to roughly estimate Gini coefficient from eye-catching Hurun Rich List and the latest poverty line. The result shows that the estimation of Gini coefficient using quintile rule is small for both urban and rural area, while the value of the whole country is obviously larger, which is above the warning line of 0.4. It is indicated that the wealth gap mainly comes from the gap between urban and rural areas. On the other hand, the estimation of Gini coefficient using curve-fitting method is as large as more than 0.7, which implies that the wealth gap is?highlighted from the analysis of the lowest and highest part of the wealth distribution. All in all, China’s current gap between the poor and the rich is serious. The reform of the income distribution needs to speed up to ensure social harmony and stability.
文摘We study the quasi likelihood equation in Generalized Linear Models(GLM) with adaptive design ∑ni=1x_i(y_i-h(x_i′β))=0, where y_i is a q-vector, and x_i is a p×q random matrix. Under some assumptions, it is shown that the Quasi-Likelihood equation for the GLM has a solution which is asymptotic normal.
基金a grant from the Technologies R & D Program of Shanghai (No. 011209014).
文摘Objective: To discover new proteomic biomarkers of hepatocellular carcinoma. Methods: Surface enhanced laser desorption/ionization time-of-flight (SELDI-TOF) mass spectrometry was used to discover biomarkers for differentiating hepatocellular carcinoma and chronic liver disease. A population of 50 patients with hepatocellular carcinoma and 33 patients with chronic liver disease was studied. Results: Twelve proteomic biomarkers of hepatocellular carcinoma were detected in this study. Three proteomic biomarkers were highly expressed in hepatocellular carcinoma and nine proteomic biomarkers were highly expressed in chronic liver disease. The most valuable proteomic biomarker with m/z=11498 had no similar diagnostic value as α-fetoprotein. Conclusion: Some of the twelve proteomic biomarkers may become new biomarkers of hepatocellular carcinoma.
基金supported by National Natural Science Foundation of China(Grant No.10371117)the Doctoral Program Foundation of Ministry of Education and the Special Foundation of USTC.
文摘For two independent non-negative random variables X and Y, we treat X as the initial variable of major importance and Y as a modifier (such as the interest rate of a portfolio).Stability in the tail behaviors of the product compared with that of the original variable X is of practical interests. In this paper, we study the tail behaviors of the product XY when the distribution of X belongs to the classes L and S, respectively. Under appropriate conditions, we show that the distribution of the product XY is in the same class as X when X belongs to class L or S, in other words, classes L and S are stable under some mild conditions on the distribution of Y. We also show that if the distribution of X is in class L(γ) (γ＞ 0) and continuous, then the product XY is in L if and only if Y is unbounded.
文摘Under very weak condition 0 【 r(t)↑∞ , t→∞. we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some results on strong law of large numbers are given such that our results are much stronger than the corresponding result of Gadidov’s.
文摘Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of interest rates becomes more important in pricing such long-dated options.In this paper,the pricing of Asian options under stochastic interest rates is studied.Assuming Hull and White model for the interest rates,a closed-form formula for geometric-average options is derived.As a by-product,pricing formula is also given for plan-vanilla options under stochastic interest rates.
基金Supported by the National Natural Science Foundation of China(61877023)the Fundamental Research Funds for the Central Universities(CCNU19TD009)。
文摘For high-dimensional models with a focus on classification performance,the?1-penalized logistic regression is becoming important and popular.However,the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data.We propose two types of weighted Lasso estimates,depending upon covariates determined by the Mc Diarmid inequality.Given sample size n and a dimension of covariates p,the finite sample behavior of our proposed method with a diverging number of predictors is illustrated by non-asymptotic oracle inequalities such as the?1-estimation error and the squared prediction error of the unknown parameters.We compare the performance of our method with that of former weighted estimates on simulated data,then apply it to do real data analysis.
基金Supported by the National Natural Science Foundation of China(11671375 and 11471303)Natural Science Foundation of Anhui Provincial Education Department(KJ2017A171)
文摘In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.
基金supported by the National Basic Research Program of China(973 Program)under Grant No.2007CB814901the National Natural Science Foundation of China under Grant Nos.11101215 and 61304065the Program of Natural Science Research of Jiangsu Higher Education Institutions of China under GrantNo.12KJB110011
文摘This paper investigates the pricing of options written on non-traded assets and trading strategies for the stock and option in an exponential utility maximization framework.Under the assumption that the option can be continuously traded without friction just as the stock,a dynamic relationship between their optimal positions is derived by using the stochastic dynamic programming techniques.The dynamic option pricing equations are also established.In particular,the properties of the associated solutions are discussed and their explicit representations are demonstrated via the Feynman-Kac formula.This paper further compares the dynamic option price to the existing price notions,such as the marginal price and indifference price.
基金This work was supported by the National Natural Science Foundation of China(Grants No.10471135 and 10271001).
文摘The strong convergence and convergence rate of the random quadratic formss1T(S1S1T)ms1 and s1T(SST)ms1 are set up. The application of these results in wireless communication is given. Simulation results are presented.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No.10471135)
文摘In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.
基金supported by the National key scientific instrument and Equipment Development Program of China under Grant No.2012YQ220119Anhui Provincial Natural Science Foundation under Grant No.1308085 MF93+1 种基金the Fundamental Research Foundation for the Central Universities under Grant No.2013HGXJ0223National Natural Science Foundations of China under Grant No.11201108
文摘The changes of numeraire can be used as a very powerful tool in pricing contingent claims in the context of a complete market.By using the method of numeraire changes to evaluate convertible bonds when the value of firm,and those of zero-coupon bonds follow general adapted stochastic processes in this paper,using Ito theorem and Gisanov theorem.A closed-form solution is derived under the stochastic volatility by using fast Fourier transforms.
