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Likelihood-based inference under nonconvex boundary constraints.

J Y Wang1, Z S Ye1, Y Chen2

  • 1Department of Industrial Systems Engineering & Management, National University of Singapore, Engineering Drive 2, 117576 Singapore.

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|May 15, 2024
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Summary
This summary is machine-generated.

This study addresses likelihood-based inference for biomedical research with complex, nonconvex parameter constraints. It provides methods for maximum likelihood estimation and likelihood ratio tests when true parameters are at the boundary.

Keywords:
Likelihood ratio testMetric projectionNonstandard condition

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Area of Science:

  • Statistics
  • Biomedical Research
  • Econometrics

Background:

  • Likelihood-based inference is crucial in biomedical research.
  • Nonconvex constraints on model parameters are increasingly common.
  • Challenges arise when true parameter values lie at the boundary of these constraints.

Purpose of the Study:

  • Establish large-sample properties of the maximum likelihood estimator under boundary conditions in nonconvex parameter spaces.
  • Derive the asymptotic distribution of the likelihood ratio test statistic under such constraints.
  • Provide a general Monte Carlo procedure for generating the limiting distribution.

Main Methods:

  • Asymptotic theory for maximum likelihood estimation.
  • Derivation of the asymptotic distribution for the likelihood ratio test statistic.
  • Development of a Monte Carlo simulation procedure for the limiting distribution.

Main Results:

  • Established large-sample properties of the maximum likelihood estimator at the boundary of nonconvex parameter spaces.
  • Derived the asymptotic distribution of the likelihood ratio test statistic under nonconvex constraints.
  • Demonstrated the applicability of the methods through five diverse examples.

Conclusions:

  • The study provides essential theoretical tools for likelihood-based inference in complex biomedical models.
  • The derived methods and procedures are applicable to various statistical and econometric problems with boundary constraints.
  • This work facilitates more accurate statistical analysis in fields utilizing constrained parameter spaces.