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Classical Testing in Functional Linear Models.

Dehan Kong1, Ana-Maria Staicu2, Arnab Maity2

  • 1Department of Biostatistics, University of North Carolina, Chapel Hill, NC, 27599, U.S.A.

Journal of Nonparametric Statistics
|September 29, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces four classical regression tests to functional linear regression for assessing the relationship between scalar responses and functional covariates. These methods are validated for accuracy and used to develop sample size calculations.

Keywords:
Asymptotic distributionFunctional linear modelFunctional principal component analysisHypothesis Testing

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Classical regression tests (Wald, score, likelihood ratio, F-tests) are fundamental in statistical analysis.
  • Functional linear regression models relationships involving functions as covariates.

Purpose of the Study:

  • To extend four traditional regression tests to the functional linear regression framework.
  • To test the null hypothesis of no association between a scalar response and a functional covariate.

Main Methods:

  • Functional principal component analysis (FPCA) is used to re-express the functional linear model.
  • The functional covariate's effect is approximated by a finite linear combination of functional principal component scores.
  • Application of Wald, score, likelihood ratio, and F-tests within this framework.

Main Results:

  • Theoretical investigation of the proposed testing procedures for densely observed functional covariates.
  • Development of a sample size calculation procedure based on the theoretical distribution of the tests.
  • Numerical comparison of the four tests using simulation experiments and real data.

Conclusions:

  • The extended testing procedures are theoretically sound and practically applicable.
  • The study provides a robust methodology for hypothesis testing in functional linear regression.
  • The findings facilitate sample size determination and comparative analysis of different testing approaches.