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An adaptive model checking test for functional linear model

  • Author / Creator
    Shi, Enze
  • 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.

  • Subjects / Keywords
  • Graduation date
    Fall 2022
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/r3-p0jx-r117
  • License
    This thesis is made available by the University of Alberta Library with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.