Statistics and Its Interface

Volume 14 (2021)

Number 4

Estimation and inference for covariate adjusted partially functional linear regression models

Pages: 359 – 371

DOI: https://dx.doi.org/10.4310/20-SII656

Authors

Zhiqiang Jiang (School of Science, Nanjing University of Science and Technology, Nanjing, China)

Zhensheng Huang (School of Science, Nanjing University of Science and Technology, Nanjing, China)

Hanbing Zhu (School of Statistics, Key Laboratory of Advanced Theory and Application in Statistics and Data Science, MOE, East China Normal University, Shanghai, China)

Abstract

In this paper, we introduce covariate adjusted partially functional linear regression models, in which both the response and the covariates in the non-functional linear component can only be observed after being distorted by some multiplicative factors. We first estimate the distorting functions by nonparametrically regressing the response variables and covariates on the distorting covariate, and then the estimators of the slope function and the partially linear coefficient are obtained using the estimated response variables and covariates and functional principal component analysis based on corrected profile least-squares. We establish the asymptotic properties of the proposed estimators. In addition, using empirical likelihood and functional principal component analysis, we construct confidence intervals and bands for the coefficient parameters and the slope function, respectively. Finally, some simulation studies and an empirical analysis of a real dataset are conducted to illustrate the finite sample performance of the proposed method.

Keywords

confidence region, corrected profile least-squares, covariate adjusted regression, functional data, functional principal component analysis, partially functional linear models

2010 Mathematics Subject Classification

Primary 62G08. Secondary 62G20.

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This research was supported by the National Natural Science Foundation of China (Grant Nos. 11471160, 11101114), the National Statistical Science Research Major Program of China (Grant No. 2018LD01), the Fundamental Research Funds for the Central Universities (Grant No. 30920130111015), sponsored by Qing Lan Project and Graduate Research Innovation Project of the Faculty Economics and Management, ECNU(2018FEM-BCKZD004).

Received 15 November 2019

Accepted 8 December 2020

Published 8 July 2021