Volume 40, Issue 1 pp. 119-132
RESEARCH ARTICLE

Kernel density-based likelihood ratio tests for linear regression models

Feifei Yan

Feifei Yan

School of Mathematics and Statistics, Central South University, Changsha, China

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Qing-Song Xu

Qing-Song Xu

School of Mathematics and Statistics, Central South University, Changsha, China

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Man-Lai Tang

Man-Lai Tang

Department of Mathematics, Statistics and Insurance, Hang Seng University of Hong Kong, Hong Kong, China

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Ziqi Chen

Corresponding Author

Ziqi Chen

School of Statistics, KLATASDS-MOE, East China Normal University, Shanghai, China

Correspondence Ziqi Chen, School of Statistics, KLATASDS-MOE, East China Normal University, Shanghai, 200062, China.

Email: [email protected]

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First published: 04 October 2020

Funding information: Innovation Program of Central South University, 2018zzts102; Research Grant Council of the Hong Kong Special Administrative Region, UGC/FDS14/P01/16; UGC/FDS14/P02/18; National Natural Science Foundation of China, 11871124; 11871477

Abstract

In this article, we develop a so-called profile likelihood ratio test (PLRT) based on the estimated error density for the multiple linear regression model. Unlike the existing likelihood ratio test (LRT), our proposed PLRT does not require any specification on the error distribution. The asymptotic properties are developed and the Wilks phenomenon is studied. Simulation studies are conducted to examine the performance of the PLRT. It is observed that our proposed PLRT generally outperforms the existing LRT, empirical likelihood ratio test and the weighted profile likelihood ratio test in sense that (i) its type I error rates are closer to the prespecified nominal level; (ii) it generally has higher powers; (iii) it performs satisfactorily when moments of the error do not exist (eg, Cauchy distribution); and (iv) it has higher probability of correctly selecting the correct model in the multiple testing problem. A mammalian eye gene expression dataset and a concrete compressive strength dataset are analyzed to illustrate our methodologies.

CONFLICT OF INTEREST

The authors declare no potential conflict of interests.

DATA AVAILABILITY STATEMENT

The mammalian eye gene expression dataset is available via the link http://myweb.uiowa.edu/pbreheny/data/Scheetz2006.html;19 The concrete compressive strength dataset is available from the UCI Machine Learning Repository via the link http://archive.ics.uci.edu/ml/datasets/Concrete+Compressive+Strength.28

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