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Generalized p-values for testing regression coefficients in partially linear models

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Abstract

The one-sided and two-sided hypotheses about the parametric component in partially linear model are considered in this paper. Generalized p-values are proposed based on fiducial method for testing the two hypotheses at the presence of nonparametric nuisance parameter. Note that the nonparametric component can be approximated by a linear combination of some known functions, thus, the partially linear model can be approximated by a linear model. Thereby, generalized p-values for a linear model are studied first, and then the results are extended to the situation of partially linear model. Small sample frequency properties are analyzed theoretically. Meanwhile, simulations are conducted to assess the finite sample performance of the tests based on the proposed p-values.

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Author information

Authors and Affiliations

  1. School of Statistics and Mathematics, Shandong University of Finance, Jinan, 250014, China

    Huimin Hu

  2. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China

    Xingzhong Xu

  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Guoying Li

Authors
  1. Huimin Hu
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  2. Xingzhong Xu
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  3. Guoying Li
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Corresponding author

Correspondence to Huimin Hu.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 10771015 and the Start-Up Funds for Doctoral Scientific Research of Shandong University of Finance.

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Hu, H., Xu, X. & Li, G. Generalized p-values for testing regression coefficients in partially linear models. J Syst Sci Complex 23, 1118–1132 (2010). https://doi.org/10.1007/s11424-010-8147-0

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  • DOI: https://doi.org/10.1007/s11424-010-8147-0

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