In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been presented.In this paper,a new depthfunction family that meets four ...In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been presented.In this paper,a new depthfunction family that meets four properties mentioned in Zuo and Serfling(2000)is proposed.Then aclassification rule based on the depth function family is proposed.The classification parameter b couldbe modified according to the type-Ⅰerrorα,and the estimator of b has the consistency and achievesthe convergence rate n^(-1/2).With the help of the proper selection for depth family parameter c,theapproach for discriminant analysis could minimize the type-Ⅱerrorβ.A simulation study and a realdata example compare the performance of the different discriminant methods.展开更多
In this paper,we mainly study the feature screening and error variance estimation in ultrahigh-dimensional linear model with errors-in-variables(EV).Given that sure independence screening(SIS)method by marginal Pearso...In this paper,we mainly study the feature screening and error variance estimation in ultrahigh-dimensional linear model with errors-in-variables(EV).Given that sure independence screening(SIS)method by marginal Pearson’s correlation learning may omit some important observation variables due to measurement errors,a corrected SIS called EVSIS is proposed to rank the importance of features according to their corrected marginal correlation with the response variable.Also,a corrected error variance procedure is proposed to accurately estimate the error variance,which could greatly attenuate the influence of measurement errors and spurious correlations,simultaneously.Under some regularization conditions,the proposed EVSIS possesses sure screening property and consistency in ranking and the corrected error variance estimator is also proved to be asymptotically normal.The two methodologies are illustrated by some simulations and a real data example,which suggests that the proposed methods perform well.展开更多
Measuring and testing tail dependence is important in finance, insurance, and risk management. This paper proposes two tail dependence matrices based on classic rank correlation coefficients,which possess the desired ...Measuring and testing tail dependence is important in finance, insurance, and risk management. This paper proposes two tail dependence matrices based on classic rank correlation coefficients,which possess the desired population properties and interpretability. Their nonparametric estimators with strong consistency and asymptotic distributions are derived using the limit theory of U-processes.The simulation and application studies show that, compared to the tail dependence matrix based on Spearman's ρ with large deviation, the Kendall-based tail dependence measure has stable variances under different tail conditions;thus, it is an effective approach to testing and quantifying tail dependence between random variables.展开更多
The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parame...The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.展开更多
In this paper,we mainly study how to estimate the error density in the ultrahigh dimensional sparse additive model,where the number of variables is larger than the sample size.First,a smoothing method based on B-splin...In this paper,we mainly study how to estimate the error density in the ultrahigh dimensional sparse additive model,where the number of variables is larger than the sample size.First,a smoothing method based on B-splines is applied to the estimation of regression functions.Second,an improved two-stage refitted crossvalidation(RCV)procedure by random splitting technique is used to obtain the residuals of the model,and then the residual-based kernel method is applied to estimate the error density function.Under suitable sparse conditions,the large sample properties of the estimator,including the weak and strong consistency,as well as normality and the law of the iterated logarithm,are obtained.Especially,the relationship between the sparsity and the convergence rate of the kernel density estimator is given.The methodology is illustrated by simulations and a real data example,which suggests that the proposed method performs well.展开更多
A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and b...A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and breakdown points are also derived. They possess the same breakdown points as the median, and some of them own higher asymptotic relative efficiencies at the heavy-tailed distributions than some other well-known location estimators; whereas the trimmed means, Winsorized means and Huber＇s M-estimator possess higher asymptotic relative efficiencies at the light-tailed distributions, in which Huber＇s M-estimator is the most robust.展开更多
In this thesis,we construct test statistic for association test and independence test in high dimension,respectively,and study the corresponding theoretical properties under some regularity conditions.Meanwhile,we pro...In this thesis,we construct test statistic for association test and independence test in high dimension,respectively,and study the corresponding theoretical properties under some regularity conditions.Meanwhile,we propose a nonparametric variable screening procedure for sparse additive model with multivariate response in untra-high dimension and established some screening properties.展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.10901020,10726013 and 10771017
文摘In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been presented.In this paper,a new depthfunction family that meets four properties mentioned in Zuo and Serfling(2000)is proposed.Then aclassification rule based on the depth function family is proposed.The classification parameter b couldbe modified according to the type-Ⅰerrorα,and the estimator of b has the consistency and achievesthe convergence rate n^(-1/2).With the help of the proper selection for depth family parameter c,theapproach for discriminant analysis could minimize the type-Ⅱerrorβ.A simulation study and a realdata example compare the performance of the different discriminant methods.
基金supported partly by the National Natural Science Foundation of China(Grant No.11971324)supported by the State Key Program of National Natural Science Foundation of China(Grant No.12031016).
文摘In this paper,we mainly study the feature screening and error variance estimation in ultrahigh-dimensional linear model with errors-in-variables(EV).Given that sure independence screening(SIS)method by marginal Pearson’s correlation learning may omit some important observation variables due to measurement errors,a corrected SIS called EVSIS is proposed to rank the importance of features according to their corrected marginal correlation with the response variable.Also,a corrected error variance procedure is proposed to accurately estimate the error variance,which could greatly attenuate the influence of measurement errors and spurious correlations,simultaneously.Under some regularization conditions,the proposed EVSIS possesses sure screening property and consistency in ranking and the corrected error variance estimator is also proved to be asymptotically normal.The two methodologies are illustrated by some simulations and a real data example,which suggests that the proposed methods perform well.
基金Supported by the State Key Program of the National Natural Science Foundation of China (Grant No. 12031016)National Natural Science Foundation of China (Grant Nos. 11971324, 11901406, 12201435)+4 种基金Beijing Postdoctoral Research Foundation (Grant No. 2022-ZZ-084)Dalian High-level Talent Innovation Project (Grant No.2020RD09)the Interdisciplinary Construction of Bioinformatics and Statisticsthe Academy for Multidisciplinary StudiesCapital Normal University
文摘Measuring and testing tail dependence is important in finance, insurance, and risk management. This paper proposes two tail dependence matrices based on classic rank correlation coefficients,which possess the desired population properties and interpretability. Their nonparametric estimators with strong consistency and asymptotic distributions are derived using the limit theory of U-processes.The simulation and application studies show that, compared to the tail dependence matrix based on Spearman's ρ with large deviation, the Kendall-based tail dependence measure has stable variances under different tail conditions;thus, it is an effective approach to testing and quantifying tail dependence between random variables.
基金supported by the Natural Science Foundation of China under Grant Nos.10771017 and 11071022Key Project of MOE,PRC under Grant No.309007
文摘The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.
基金supported by National Natural Science Foundation of China (Grant Nos. 11971324 and 11471223)Interdisciplinary Construction of Bioinformatics and StatisticsAcademy for Multidisciplinary Studies, Capital Normal University
文摘In this paper,we mainly study how to estimate the error density in the ultrahigh dimensional sparse additive model,where the number of variables is larger than the sample size.First,a smoothing method based on B-splines is applied to the estimation of regression functions.Second,an improved two-stage refitted crossvalidation(RCV)procedure by random splitting technique is used to obtain the residuals of the model,and then the residual-based kernel method is applied to estimate the error density function.Under suitable sparse conditions,the large sample properties of the estimator,including the weak and strong consistency,as well as normality and the law of the iterated logarithm,are obtained.Especially,the relationship between the sparsity and the convergence rate of the kernel density estimator is given.The methodology is illustrated by simulations and a real data example,which suggests that the proposed method performs well.
基金This research is supported by the National Natural Science Foundation of China （Grant No. 10371012, 10231030,and 40574020）.
文摘A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and breakdown points are also derived. They possess the same breakdown points as the median, and some of them own higher asymptotic relative efficiencies at the heavy-tailed distributions than some other well-known location estimators; whereas the trimmed means, Winsorized means and Huber＇s M-estimator possess higher asymptotic relative efficiencies at the light-tailed distributions, in which Huber＇s M-estimator is the most robust.
文摘In this thesis,we construct test statistic for association test and independence test in high dimension,respectively,and study the corresponding theoretical properties under some regularity conditions.Meanwhile,we propose a nonparametric variable screening procedure for sparse additive model with multivariate response in untra-high dimension and established some screening properties.
