Tests for p -regression Coefficients in Linear Panel Model When p is Divergent
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Acta Mathemacae Applicatae Sinica, English Series The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2020
Tests for p-regression Coefficients in Linear Panel Model When p is Divergent Jing ZHAO1,2 , Mi-xia WU2 , Wei-hu CHENG2,† , Yao-hua RONG2 , Yu-ping HU3 1 China
National Institute of Standardization, Beijing 100191, China of Applied Sciences, Beijing University of Technology, Beijing, 100124, China
2 College
(† E-mail: [email protected]) 3 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
Abstract
This paper evaluates the performance of the FW -test for testing part of p-regression coefficients
in linear panel data model when p is divergent. The asymptotic power of the FW -statistic is obtained under some regular conditions. The theoretical development are challenging since the number of covariates increases as the sample size increases. It is worth noting that the inference approach does not require any specification of the error distribution. Some simulation comparisons are conducted and show that the simulated power coincide with theoretical power well. The method is also illustrated using a renal cancer data example.
Keywords
regression coefficient; FW -statistic; Panel data
2000 MR Subject Classification
1
62J05; 62F03
Introduction
Panel data, known as longitudinal or cross-sectional time-series data, are one class data in which the behavior of entities is observed across time. These entities could be states, companies, individuals, countries, etc. With the increasing availability of panel data, both theory and applied works in this field have become more and more popular in recent years. Two excellent overviews of parametric panel data analysis are provided by [4, 7]. Along with the technical development, the econometricians and statisticians have paid much attention on high-dimensional data recently. One important essence of the high dimensional data under the regression setting lies in that the number of covariates may grow with the sample size. So here high-dimension we refer actually means the dimension of covariates is divergent. The research on high dimensional data alone has created the need of reexamining some of the conventional analysis procedures, since the classical large sample theories are based on the condition that the dimension of covariates is fixed and the sample size tends to infinity. There have been a series of important studies on high dimensional problem. Portnoy[15, 16] had investigated the consistency and asymptotic normality for the M-estimators of linear regression coefficients under the condition that the dimension p of the covariates grows to infinity faster than the square root of the sample size n. Kosorok and Ma[13] considered uniform convergence for a large number of marginal discrepancy measures for univariate distribution. Fan and Li[8] , Huang, Horowitz and Ma[10] , Huang, Ma and Zhang[11] considered covariates selection procedures for high-dimensional linear regression. By variable selection we can choose the Manus
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