Partially Functional Linear Models with Linear Process Errors

Yanping Hu () and Zhongqi Pang
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Yanping Hu: School of Mathematical Sciences, Tongji University, Shanghai 200092, China
Zhongqi Pang: Department of Applied Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China

Mathematics, 2023, vol. 11, issue 16, 1-18

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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