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Volume 11
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Article

Partially Functional Linear Models with Linear Process Errors

by
Yanping Hu
1,* and
Zhongqi Pang
2
1
School of Mathematical Sciences, Tongji University, Shanghai 200092, China
2
Department of Applied Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(16), 3581; https://doi.org/10.3390/math11163581
Submission received: 20 July 2023 / Revised: 10 August 2023 / Accepted: 15 August 2023 / Published: 18 August 2023
(This article belongs to the Special Issue Statistical Modeling for Analyzing Data with Complex Structures)
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Abstract

In this paper, we focus on the partial functional linear model with linear process errors deduced by not necessarily independent random variables. Based on Mercer’s theorem and Karhunen–Loève expansion, we give the estimators of the slope parameter and coefficient function in the model, establish the asymptotic normality of the estimator for the parameter and discuss the weak convergence with rates of the proposed estimators. Meanwhile, the penalized estimator of the parameter is defined by the SCAD penalty and its oracle property is investigated. Finite sample behavior of the proposed estimators is also analysed via simulations.
Keywords: symptotic normality; convergence rate; linear process error; partial functional linear model; variable selection symptotic normality; convergence rate; linear process error; partial functional linear model; variable selection

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MDPI and ACS Style

Hu, Y.; Pang, Z. Partially Functional Linear Models with Linear Process Errors. Mathematics 2023, 11, 3581. https://doi.org/10.3390/math11163581

AMA Style

Hu Y, Pang Z. Partially Functional Linear Models with Linear Process Errors. Mathematics. 2023; 11(16):3581. https://doi.org/10.3390/math11163581

Chicago/Turabian Style

Hu, Yanping, and Zhongqi Pang. 2023. "Partially Functional Linear Models with Linear Process Errors" Mathematics 11, no. 16: 3581. https://doi.org/10.3390/math11163581

APA Style

Hu, Y., & Pang, Z. (2023). Partially Functional Linear Models with Linear Process Errors. Mathematics, 11(16), 3581. https://doi.org/10.3390/math11163581

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