Weighted composite asymmetric Huber estimation for partial functional linear models

Juxia Xiao; Ping Yu; Zhongzhan Zhang; Juxia Xiao; Ping Yu; Zhongzhan Zhang

doi:10.3934/math.2022430

AIMS Mathematics

2022, Volume 7, Issue 5: 7657-7684. doi: 10.3934/math.2022430

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Research article

Weighted composite asymmetric Huber estimation for partial functional linear models

1.
Faculty of Science, Beijing University of Technology, Beijing 100124, China
2.
School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030000, China

Received: 01 December 2021 Revised: 19 January 2022 Accepted: 24 January 2022 Published: 16 February 2022
MSC : 62G05, 62G20

In this paper, we first investigate a new asymmetric Huber regression (AHR) estimation procedure to analyze skewed data with partial functional linear models. To automatically reflect distributional features as well as bound the influence of outliers effectively, we further propose a weighted composite asymmetric Huber regression (WCAHR) estimation procedure by combining the strength across multiple asymmetric Huber loss functions. The slope function and constant coefficients are estimated through minimizing the combined loss function and approximating the slope function with principal component analysis. The asymptotic properties of the proposed estimators are derived. To realize the WCAHR estimation, we also develop a practical algorithm based on pseudo data. Numerical results show that the proposed WCAHR estimators can well adapt to the different error distributions, and thus are more useful in practice. Two real data examples are presented to illustrate the applications of the proposed methods.
Citation: Juxia Xiao, Ping Yu, Zhongzhan Zhang. Weighted composite asymmetric Huber estimation for partial functional linear models[J]. AIMS Mathematics, 2022, 7(5): 7657-7684. doi: 10.3934/math.2022430

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Abstract

In this paper, we first investigate a new asymmetric Huber regression (AHR) estimation procedure to analyze skewed data with partial functional linear models. To automatically reflect distributional features as well as bound the influence of outliers effectively, we further propose a weighted composite asymmetric Huber regression (WCAHR) estimation procedure by combining the strength across multiple asymmetric Huber loss functions. The slope function and constant coefficients are estimated through minimizing the combined loss function and approximating the slope function with principal component analysis. The asymptotic properties of the proposed estimators are derived. To realize the WCAHR estimation, we also develop a practical algorithm based on pseudo data. Numerical results show that the proposed WCAHR estimators can well adapt to the different error distributions, and thus are more useful in practice. Two real data examples are presented to illustrate the applications of the proposed methods.

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