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Generalized F-test for high dimensional regression coefficients of partially linear models

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Abstract

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.

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Authors and Affiliations

  1. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081, China

    Siyang Wang & Hengjian Cui

  2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Siyang Wang & Hengjian Cui

Authors
  1. Siyang Wang
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  2. Hengjian Cui
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Corresponding author

Correspondence to Hengjian Cui.

Additional information

This research was supported by the Natural Science Foundation of China under Grant Nos. 11231010, 11471223, 11501586, BCMIIS and Key Project of Beijing Municipal Educational Commission under Grant No. KZ201410028030.

This paper was recommended for publication by Editor DONG Yuexiao.

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Wang, S., Cui, H. Generalized F-test for high dimensional regression coefficients of partially linear models. J Syst Sci Complex 30, 1206–1226 (2017). https://doi.org/10.1007/s11424-017-6012-0

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  • DOI: https://doi.org/10.1007/s11424-017-6012-0

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