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Author:

Lai, Tingyu (Lai, Tingyu.) | Zhang, Zhongzhan (Zhang, Zhongzhan.) (Scholars:张忠占) | Wang, Yafei (Wang, Yafei.)

Indexed by:

Scopus SCIE

Abstract:

A conventional regression model for functional data involves expressing a response variable in terms of the predictor function. Two assumptions, that (i) the predictor function and the error are independent and (ii) the relationship between the response variable and the predictor function takes functional linear model, are usually added to the model. Checking the validation of these two assumptions is fundamental to statistic inference and practical applications. We develop a test procedure to check these assumptions simultaneously based on generalized distance covariance. We establish the asymptotic theory for the proposed test under null and alternative hypotheses, and provide a bootstrap procedure to obtain the critical value of the test. The proposed test is consistent against all alternatives provided that the semimetrics related to the generalized distance are strong negative, and can be readily generalized to other functional regression models. We explore the finite sample performance of the proposed test by using both simulations and real data examples. The results illustrate that the proposed method has favorable performance compared with the competing method.

Keyword:

Independence test Strong negative type space Goodness-of-fit Generalized distance covariance Functional linear model

Author Community:

  • [ 1 ] [Lai, Tingyu]Beijing Univ Technol, Fac Sci, Beijing 100124, Peoples R China
  • [ 2 ] [Zhang, Zhongzhan]Beijing Univ Technol, Fac Sci, Beijing 100124, Peoples R China
  • [ 3 ] [Wang, Yafei]Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2R3, Canada

Reprint Author's Address:

  • 张忠占

    [Zhang, Zhongzhan]Beijing Univ Technol, Fac Sci, Beijing 100124, Peoples R China

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Source :

JOURNAL OF THE KOREAN STATISTICAL SOCIETY

ISSN: 1226-3192

Year: 2020

Issue: 2

Volume: 50

Page: 380-402

0 . 6 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:46

Cited Count:

WoS CC Cited Count: 3

SCOPUS Cited Count: 5

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 5

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