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Imputation based statistical inference for partially linear quantile regression models with missing responses

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Abstract

In this paper, we consider the confidence interval construction for partially linear quantile regression models with missing response at random. We propose an imputation based empirical likelihood method to construct confidence intervals for the parametric components and the nonparametric components, and show that the proposed empirical log-likelihood ratios are both asymptotically Chi-squared in theory. Then, the confidence region for the parametric component and the pointwise confidence interval for the nonparametric component are constructed. Some simulation studies and a real data application are carried out to assess the performance of the proposed estimation method, and simulation results indicate that the proposed method is workable.

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Acknowledgments

The authors sincerely thank the referees and the editor for their constructive suggestions and comments, which substantially improved an earlier version of this paper. This paper is supported by the National Natural Science Foundation of China (11301569), the Chongqing Research Program of Basic Theory and Advanced Technology (cstc2015jcyjA00023), the Research Foundation of Chongqing Municipal Education Commission (KJ1500614), and the Scientific Research Foundation of Chongqing Technology and Business University (2015-56-06).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Peixin Zhao

  2. Department of Logistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Xinrong Tang

Authors
  1. Peixin Zhao
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  2. Xinrong Tang
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Correspondence to Peixin Zhao.

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Zhao, P., Tang, X. Imputation based statistical inference for partially linear quantile regression models with missing responses. Metrika 79, 991–1009 (2016). https://doi.org/10.1007/s00184-016-0586-8

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  • DOI: https://doi.org/10.1007/s00184-016-0586-8

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