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Robust comparison of regression curves

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Abstract

This paper is concerned about robust comparison of two regression curves. Most of the procedures in the literature are least-squares-based methods with local polynomial approximation to nonparametric regression. However, the efficiency of these methods is adversely affected by outlying observations and heavy-tailed distributions. To attack this challenge, a robust testing procedure is recommended under the framework of the generalized likelihood ratio test (GLR) by incorporating with a Wilcoxon-type artificial likelihood function. Under the null hypothesis, the proposed test statistic is proved to be asymptotically normal and free of nuisance parameters and covariate designs. Its asymptotic relative efficiency with respect to the least-squares-based GLR method is closely related to that of the signed-rank Wilcoxon test in comparison with the \(t\) test. We then consider a bootstrap approximation to determine \(p\) values of the test in finite sample situation. Its asymptotic validity is also presented. A simulation study is conducted to examine the performance of the proposed test and to compare it with its competitors in the literature.

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Acknowledgments

The authors thank the editor, associate editor and two anonymous referees for their many helpful comments that have resulted in significant improvements in the article. Long Feng and Lixing Zhu were partly supported by a grant from the University Grants Council of Hong Kong, China when Long Feng visited Hong Kong Baptist University. Changliang Zou and Zhaojun Wang were supported by the NNSF of China Grants 11131002, 11101306, 11371202, 71202087, the RFDP of China Grant 20110031110002, the Foundation for the Author of National Excellent Doctoral Dissertation of PR China 201232, New Century Excellent Talents in University and PAPD of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. Institute of Statistics, Nankai University, Tianjin, China

    Long Feng, Changliang Zou & Zhaojun Wang

  2. Department of Mathematics, Hong Kong Baptist University, Hong Kong, Hong Kong

    Lixing Zhu

Authors
  1. Long Feng
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  2. Changliang Zou
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  3. Zhaojun Wang
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  4. Lixing Zhu
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Correspondence to Lixing Zhu.

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Feng, L., Zou, C., Wang, Z. et al. Robust comparison of regression curves. TEST 24, 185–204 (2015). https://doi.org/10.1007/s11749-014-0394-2

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