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RCV-based error density estimation in the ultrahigh dimensional additive model

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Science China Mathematics 2022年第5期65卷 1003-1028页

作者： Feng Zou hengjian cui School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

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.

关键词： ultrahigh dimensional additive model B-spline kernel density estimation refitted cross-validation method asymptotic property

A class of robust independence tests based on weighted integrals of empirical characteristic functions

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Acta Mathematica Sinica,English Series 2023年

作者： Feng ZOU Changliang ZOU hengjian cui School of Statistics and Data Science Nankai University School of Mathematical Sciences Capital Normal University

In this paper, we propose a class of robust independence tests for two random vectors based on weighted integrals of empirical characteristic functions. By letting weight functions be probability density functions of a class of special distributions, the proposed test statistics have simple closed forms and do not require moment conditions on the random vectors. Moreover, we derive the asymptotic distributions of the test statistics under the null hypothesis. The proposed testing method is computationally feasible and easy to implement. Based on a data-driven bandwidth selection method, Monte Carlo simulation studies indicate that our tests have a relatively good performance compared with the competitors. A real data example is also presented to illustrate the application of our tests.

关键词：

ON WEIGHTED RANDOMLY TRIMMED MEANS

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Journal of Systems Science & Complexity 2007年第1期20卷 47-65页

作者： Ting WANG Yong LI hengjian cui School of Mathematical Sciences Statistical Data Analysis Laboratory Beijing Normal University Beijing 100875 China Institute of Information Sciences and Technology Massey University Private Bag 11222 Palmerston North New Zealand. School of Mathematical Sciences Statistical Data Analysis Laboratory Beijing Normal University Beijing 100875 China.

称为介绍的加权的随机整修的 meansare 和不仅他们的一致性和 asymptotic 规度的柔韧的地点评估者的一个班被证明，但是 theirinfluence 工作 asymptotic 变化和故障点也被导出。他们拥有是的 thesame 故障点中部，并且他们中的一些拥... 详细信息

称为介绍的加权的随机整修的 meansare 和不仅他们的一致性和 asymptotic 规度的柔韧的地点评估者的一个班被证明，但是 theirinfluence 工作 asymptotic 变化和故障点也被导出。他们拥有是的 thesame 故障点中部，并且他们中的一些拥有更高的 asymptotic 亲戚效率 atthe 重尾巴的分布比一些另外的著名地点评估者；而 trimmedmeans， Winsorized 工具和 Huber “ s M 评估者拥有更高的 asymptotic 亲戚效率 atthe 跟踪光的分布，在哪个 Huber ” s M 评估者是最柔韧的。

关键词：加权随机平衡均数渐进正态性分布函数崩溃点

EMPIRICAL LIKELIHOOD CONFIDENCE REGION FOR PARAMETERS IN LINEAR ERRORS-IN-VARIABLES MODELS WITH MISSING DATA

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Journal of Systems Science & Complexity 2011年第3期24卷 540-553页

作者： Juan ZHANG hengjian cui Department of Statistics Capital University of Economics and Business Beijing 100070 China. Department of Statistics and Financial MatheTnatics School of Mathematical Sciences Beijing Normal University Beijing 100875 China School of Mathematical Sciences Capital Normal University Beijing 100048 China

multivariate 线性 errors-in-variables 模型 regressors 什么时候在在 Rubin (1976 ) 的意义的随机是失踪的，在这份报纸被考虑。为 0 在这建模的一个参数的一个抑制实验可能性的信心区域被建议，它被基于反的概率把相应于加权的摆平... 详细信息

multivariate 线性 errors-in-variables 模型 regressors 什么时候在在 Rubin (1976 ) 的意义的随机是失踪的，在这份报纸被考虑。为 0 在这建模的一个参数的一个抑制实验可能性的信心区域被建议，它被基于反的概率把相应于加权的摆平的直角的距离的 20 个函数与 0 的一个抑制区域相结合构造。在真参数的实验木头可能性的比率收敛到标准 chi 平方分发，这被显示出。模拟证明建议信心区域的范围率接近名字的水平，信心间隔的长度是比反的概率的正常近似的那些狭窄的在大多数情况中的加权的调整最不方形的评估者。一个真实例子被学习，结果支持理论和模拟结论。

关键词：置信区间经验似然模型参数线性误差仿真结果加权调整回归模型逆概率

The abstract of doctoral dissertation‘Some research on hypothesis testing and nonparametric variable screening problems for high dimensional data’

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Statistical Theory and Related Fields 2020年第2期4卷 228-229页

作者： Yongshuai Chen hengjian cui School of Mathematical Sciences Capital Normal UniversityBeijingPeople’s Republic of China School of Statistics Capital University of Economics and BusinessBeijingPeople’s Republic of China

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.

关键词： High-dimensional test independence test distance correlation power enhancement association test U-statistic nonparametric variable screening additive model

Estimation in partial linear EV models with replicated observations

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Science China Mathematics 2004年第1期47卷 144-159页

作者： cui hengjian Department of Mathematics Statistical Data Analysis Laboratory Beijing Normal University Beijing 100875China

The aim of this work is to construct the parameter estimators in the partial linear errors-in-variables (EV) models and explore their asymptotic properties. Unlike other related References, the assumption of known error covariance matrix is removed when the sample can be repeatedly drawn at each designed point from the model. The estimators of interested regression parameters, and the model error variance, as well as the nonparametric function, are constructed. Under some regular conditions, all of the estimators prove strongly consistent. Meanwhile, the asymptotic normality for the estimator of regression parameter is also presented. A simulation study is reported to illustrate our asymptotic results.

关键词： partial linear EV model, strong consistency, replicated observations.

Generalized F-Test for High Dimensional Regression Coefficients of Partially Linear Models

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Journal of Systems Science & Complexity 2017年第5期30卷 1206-1226页

作者： WANG Siyang cui hengjian School of Statistics and Mathematics Central University of Finance and EconomicsBeijing 100081China School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions. During this procedure, the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test. The authors obtain some asymptotic properties of the generalized F-test in more general cases,including the asymptotic normality and the power of this test with p/n ∈(0, 1) without normality assumption. The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models. Through simulation studies, the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results. The practical utility of our method is illustrated by a real data example.

关键词：概括 F-test 高维的回归部分线性的模型测试的力量

Consistency of Chi-Squared Test with Varying Number of Classes

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Journal of Systems Science & Complexity 2015年第2期28卷 439-450页

作者： HUANG Rui cui hengjian College of Mathematic and Statistics Jishou University School of Mathematical Sciences Beijing Normal University Department of Statistics School of Mathematical SciencesCapital Normal University

The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.

关键词：卡方检验一致性检验统计量同数同时检验渐近性质随机变量收敛速度

Robust estimation for partially linear models with large-dimensional covariates

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Science China Mathematics 2013年第10期56卷 2069-2088页

作者： ZHU LiPing LI RunZe cui hengjian School of Statistics and Management Shanghai University of Finance and Economics The Key Laboratory of Mathematical Economics (SUFE) Ministry of Education Department of Statistics and The Methodology Center The Pennsylvania State UniversityUniversity Park School of Mathematical Science Capital Normal University

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a nonconcave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(n1/2), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance.Comprehensive simulation studies are carried out and an application is presented to examine the fnite-sample performance of the proposed procedures.

关键词：部分线性模型鲁棒估计协变量 oracle 稳健估计线性组件参数估计样本大小