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Statistical inference in the partial functional linear expectile regression model

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Abstract

As extensions of means, expectiles embrace all the distribution information of a random variable. The expectile regression is computationally friendlier because the asymmetric least square loss function is differentiable everywhere. This regression also enables effective estimation of the expectiles of a response variable when potential explanatory variables are given. In this study, we propose the partial functional linear expectile regression model. The slope function and constant coefficients are estimated by using the functional principal component basis. The convergence rate of the slope function and the asymptotic normality of the parameter vector are established. To inspect the effect of the parametric component on the response variable, we develop Wald-type and expectile rank score tests and establish their asymptotic properties. The finite performance of the proposed estimators and test statistics are evaluated through simulation study. Results indicate that the proposed estimators are comparable to competing estimation methods and the newly proposed expectile rank score test is useful. The methodologies are illustrated by using two real data examples.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11771032), Natural Science Foundation of Shanxi Province of China (Grant No. 201901D111279) and the Research Grant Council of the Hong Kong Special Administration Region (Grant Nos. 14301918 and 14302519). The authors thank the two anonymous referees for their helpful comments and suggestions that improved the article substantially.

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Authors and Affiliations

  1. Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Juxia Xiao & Zhongzhan Zhang

  2. School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, 030092, China

    Juxia Xiao & Ping Yu

  3. Department of Statistics, The Chinese University of Hong Kong, Hong Kong, 999077, China

    Xinyuan Song

Authors
  1. Juxia Xiao
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  2. Ping Yu
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  3. Xinyuan Song
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  4. Zhongzhan Zhang
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Correspondence to Xinyuan Song.

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Xiao, J., Yu, P., Song, X. et al. Statistical inference in the partial functional linear expectile regression model. Sci. China Math. 65, 2601–2630 (2022). https://doi.org/10.1007/s11425-020-1848-8

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  • DOI: https://doi.org/10.1007/s11425-020-1848-8

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