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Empirical Likelihood Test for Regression Coefficients in High Dimensional partially linear models

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Journal of Systems Science & Complexity 2021年第3期34卷 1135-1155页

作者： LIU Yan REN Mingyang ZHANG Sanguo School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Key Laboratory of Big Data Mining and Knowledge Management Chinese Academy of SciencesBeijing 100190China

This paper considers tests for regression coefficients in high dimensional partially linear *** authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly ***,the authors propose an empirical likelihood method to test regression *** authors derive the asymptotic chi-squared distribution with two degrees of freedom of the proposed test statistics under the null *** addition,the method is extended to test with nuisance *** show that the proposed method have a good performance in control of type-I error rate and *** proposed method is also employed to analyze a data of Skin Cutaneous Melanoma(SKCM).

关键词： Empirical likelihood test high dimensional analysis partially linear models regression coefficients

Precise Asymptotics of Error Variance Estimator in partially linear models

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Acta Mathematicae Applicatae Sinica 2008年第1期24卷 59-74页

作者： Shao-jun Guo, Min Chen, Feng Liu Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China Department of Statistics, Chongqing Institute of Technology, Chongqing 630000, China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Statistics Chongqing Institute of Technology Chongqing China

In this paper, we focus our attention on the precise asymptotics of error variance estimator in partially linear regression models, yi = xiτβ+ g(ti) +εi, 1≤i≤n, {εi,i = 1,…, n} are i.i.d random errors with mean 0 and positive finite varianceσ2. Following the ideas of Allan Gut and Aurel Spatarut and Zhang, on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm, respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.

关键词： Precise asymptotics partially linear models error variance estimator

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 noncon- cave 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（√n）, 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 finite-sample performance of the proposed procedures.

关键词： partially linear models robust model selection smoothly clipped absolute deviation (SCAD) semiparametric models

The Application and Property of Elastic Net Procedure for partially linear models

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Chinese Quarterly Journal of Mathematics 2020年第3期35卷 290-301页

作者： HUANG Deng-xiang LI Chun-hong QIN Chao-yong LU Chun-ting Guangxi Financial Vocational College Nanning 530007China School of Mathematics and Information Sciences Guangxi UniversityNanning 530004China

Variable selection plays an important role in high-dimensional data *** the high-dimensional data often induces the strongly correlated variables problem,which should be properly *** this paper,we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate.A simulation study shows that the Elastic Net procedure deals with the strongly correlated variables problem better than the Lasso,ALasso and the Ridge *** on the real world data study,we can get that the Elastic Net procedure is particularly useful when the number of predictors pffis much bigger than the sample size n.

关键词： Elastic Net partially linear models group effect Lasso ALasso

Estimation of Parameters of partially linear Errors-in-variables models with Replicated Net Points of Observation

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Acta Mathematicae Applicatae Sinica 2006年第1期22卷 33-42页

作者： Jun-ling Ma Ke-fa Wu Research Center of Applied Statistics Shanghai University of Financc and economics Shanghai 200433 China Department of Information and Computing Science The Second Northwest University for Nationalities Ningxia 750021 China

A kind of partially linear errors-in-variables models with replicated net points of observation are studied in this paper. Estimators of unknown parameters are given. Under certain regular conditions, it is shown that... 详细信息

关键词： Errors-in-variables net points of observation partially linear models replication consistency