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Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression

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Abstract

This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression, which combines the common linear model with the functional linear regression model. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases. The slope function is fitted by B-spline. Under suitable conditions, the authors obtain the convergence rates and asymptotic normality of the estimators. Finally, simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method. Both the simulation results and the real data analysis confirm that the newly proposed method works very well.

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Author information

Authors and Affiliations

  1. School of Mathematics and Computer Science, Shanxi Normal University, Linfen, 041000, China

    Ping Yu, Jianhong Shi & Xikai Ai

  2. Department of Statistics, Fudan University, Shanghai, 200433, China

    Ping Yu & Zhongyi Zhu

Authors
  1. Ping Yu
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  2. Zhongyi Zhu
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  3. Jianhong Shi
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  4. Xikai Ai
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Corresponding author

Correspondence to Ping Yu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11671096, 11690013, 11731011.

This paper was recommended for publication by Editor TANG Niansheng.

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Yu, P., Zhu, Z., Shi, J. et al. Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression. J Syst Sci Complex 33, 527–544 (2020). https://doi.org/10.1007/s11424-020-8217-x

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  • DOI: https://doi.org/10.1007/s11424-020-8217-x

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