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On pseudolikelihood inference for semiparametric models with boundary problems.

Y Chen1,2,3,4,5, J Ning1,2,3,4,5, Y Ning1,2,3,4,5

  • 1Department of Biostatistics and Epidemiology, University of Pennsylvania, 210 Blockley Hall, 423 Guardian Drive, Philadelphia, Pennsylvania 19104, U.S.A.

Biometrika
|February 13, 2018
PubMed
Summary
This summary is machine-generated.

This study establishes the asymptotic behavior of pseudolikelihood ratio statistics in semiparametric models. The findings are crucial for hypothesis testing, particularly when parameters are at the boundary of their space.

Keywords:
Likelihood ratio testMultivariate survival modelPseudolikelihoodSemiparametric model

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Semiparametric models are widely used in statistical inference.
  • Pseudolikelihood estimation offers a practical approach for complex models.
  • Inference for parameters at the boundary of the parameter space presents unique challenges.

Purpose of the Study:

  • To establish the asymptotic behavior of the pseudolikelihood ratio statistic in semiparametric models.
  • To analyze hypothesis testing for parameters of interest on the boundary of their parameter space.
  • To investigate the relationship between pseudolikelihood and likelihood ratio statistics.

Main Methods:

  • Developing theoretical frameworks for pseudolikelihood ratio statistics.
  • Establishing asymptotic equivalence with likelihood ratio statistics under specific conditions.
  • Utilizing simulation studies to assess finite-sample performance.

Main Results:

  • The asymptotic distributions of the pseudolikelihood ratio statistic are characterized.
  • Equivalence is shown between pseudolikelihood ratio and likelihood ratio statistics for a misspecified normal model.
  • Asymptotic distributions are identified as mixtures of chi-squared variables in studied examples.

Conclusions:

  • The pseudolikelihood ratio test demonstrates robust performance in finite samples.
  • The theoretical results provide a foundation for hypothesis testing in semiparametric settings.
  • This work contributes to the understanding of statistical inference with nuisance parameters.