A U-Statistic for Testing Lack of Dependence in Functional Partially Linear Regression Model

Fanrong Zhao; Baoxue Zhang

doi:10.20944/preprints202407.1547.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 18 July 2024 / Approved: 18 July 2024 / Online: 18 July 2024 (17:26:02 CEST)

Functional partially linear regression model, contains a functional linear part and a non-parametric part, in which testing the linear relationship between the response and the functional predictor is of fundamental importance. When functional data cannot be approximated with a few principal components, based on a pseudo estimate for the unknown non-parametric component, we develop a U-statistic of order-two in this paper. Under some regularity conditions, we use the martingale central limit theorem to prove that the proposed test statistic is asymptotically normal. The finite sample performance with simulation studies and real data application are assessed to verify the proposed test procedure.

Asymptotic normality; Functional partially linear regression model; Nadaraya-Watson estimate; U-statistic

Computer Science and Mathematics, Probability and Statistics

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A U-Statistic for Testing Lack of Dependence in Functional Partially Linear Regression Model

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