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Composite Quantile Estimation in Partial Functional Linear Regression Model Based on Polynomial Spline

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Abstract

In this paper, we consider composite quantile regression for partial functional linear regression model with polynomial spline approximation. Under some mild conditions, the convergence rates of the estimators and mean squared prediction error, and asymptotic normality of parameter vector are obtained. Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least-squares based method when there are outliers in the dataset or the random error follows heavy-tailed distributions. Finally, we apply the proposed methodology to a spectroscopic data sets to illustrate its usefulness in practice.

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Acknowledgements

We thank two referees for their constructive comments that have led to a substantial improvement of the paper.

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Authors and Affiliations

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

    ** Yu & Jian Hong Shi

  2. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, 200433, P. R. China

    Ting Li

  3. Department of Statistics, Fudan University, Shanghai, 200433, P. R. China

    Zhong Yi Zhu

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  1. ** Yu
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  2. Ting Li
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  3. Zhong Yi Zhu
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  4. Jian Hong Shi
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Corresponding author

Correspondence to ** Yu.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 11671096, 11690013, 11731011 and 12071267) and the Natural Science Foundation of Shanxi Province, China (Grant No. 201901D111279)

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Yu, P., Li, T., Zhu, Z.Y. et al. Composite Quantile Estimation in Partial Functional Linear Regression Model Based on Polynomial Spline. Acta. Math. Sin.-English Ser. 37, 1627–1644 (2021). https://doi.org/10.1007/s10114-021-9172-8

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  • DOI: https://doi.org/10.1007/s10114-021-9172-8

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