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Author:

Shi, Enze (Shi, Enze.) | Liu, Yi (Liu, Yi.) | Sun, Ke (Sun, Ke.) | Li, Lingzhu (Li, Lingzhu.) | Kong, Linglong (Kong, Linglong.)

Indexed by:

Scopus SCIE

Abstract:

Numerous studies have been devoted to the estimation and inference problems for functional linear models (FLM). However, few works focus on model checking problem that ensures the reliability of results. Limited tests in this area do not have tractable null distributions or asymptotic analysis under alternatives. Also, the functional predictor is usually assumed to be fully observed, which is impractical. To address these problems, we propose an adaptive model checking test for FLM. It combines regular moment-based and conditional moment-based tests, and achieves model adaptivity via the dimension of a residual-based subspace. The advantages of our test are manifold. First, it has a tractable chi-squared null distribution and higher powers under the alternatives than its components. Second, asymptotic properties under different underlying models are developed, including the unvisited local alternatives. Third, the test statistic is constructed upon finite grid points, which incorporates the discrete nature of collected data. We develop the desirable relationship between sample size and number of grid points to maintain the asymptotic properties. Besides, we provide a data-driven approach to estimate the dimension leading to model adaptivity, which is promising in sufficient dimension reduction. We conduct comprehensive numerical experiments to demonstrate the advantages the test inherits from its two simple components.

Keyword:

sufficient reproducing kernel Hilbert space dimension reduction functional linear model Adaptive-to-model test

Author Community:

  • [ 1 ] [Shi, Enze]Univ Alberta, Dept Math & Stat Sci, Edmonton, AB, Canada
  • [ 2 ] [Liu, Yi]Univ Alberta, Dept Math & Stat Sci, Edmonton, AB, Canada
  • [ 3 ] [Sun, Ke]Univ Alberta, Dept Math & Stat Sci, Edmonton, AB, Canada
  • [ 4 ] [Kong, Linglong]Univ Alberta, Dept Math & Stat Sci, Edmonton, AB, Canada
  • [ 5 ] [Li, Lingzhu]Beijing Univ Technol, Sch Math Stat & Mech, Beijing, Peoples R China

Reprint Author's Address:

  • [Shi, Enze]Univ Alberta, Dept Math & Stat Sci, Edmonton, AB, Canada

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Source :

BERNOULLI

ISSN: 1350-7265

Year: 2025

Issue: 2

Volume: 31

Page: 894-921

1 . 5 0 0

JCR@2022

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count: 1

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 8

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