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M-Estimation for partially functional linear regression model based on splines

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  • Jianjun Zhou
  • Jiang Du
  • Zhimeng Sun

Abstract

M-estimation is a widely used technique for robust statistical inference. In this paper, we study robust partially functional linear regression model in which a scale response variable is explained by a function-valued variable and a finite number of real-valued variables. For the estimation of the regression parameters, which include the infinite dimensional function as well as the slope parameters for the real-valued variables, we use polynomial splines to approximate the slop parameter. The estimation procedure is easy to implement, and it is resistant to heavy-tailederrors or outliers in the response. The asymptotic properties of the proposed estimators are established. Finally, we assess the finite sample performance of the proposed method by Monte Carlo simulation studies.

Suggested Citation

  • Jianjun Zhou & Jiang Du & Zhimeng Sun, 2016. "M-Estimation for partially functional linear regression model based on splines," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(21), pages 6436-6446, November.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:21:p:6436-6446
    DOI: 10.1080/03610926.2014.921309
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    Cited by:

    1. Guodong Shan & Yiheng Hou & Baisen Liu, 2020. "Bayesian robust estimation of partially functional linear regression models using heavy-tailed distributions," Computational Statistics, Springer, vol. 35(4), pages 2077-2092, December.
    2. Fanrong Zhao & Baoxue Zhang, 2024. "A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model," Mathematics, MDPI, vol. 12(16), pages 1-24, August.

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