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Profile Likelihood for Hierarchical Models Using Data Doubling.

Subhash R Lele1

  • 1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2R3, Canada.

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Summary
This summary is machine-generated.

This study introduces a novel computational method for profile likelihood inference in hierarchical models. The data doubling technique simplifies complex calculations, enabling accurate statistical analysis of functions of parameters.

Keywords:
Laplace approximationdata cloningfunctions of parametersnuisance parametersparameterization invariance

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Area of Science:

  • Statistics
  • Computational Statistics
  • Statistical Modeling

Background:

  • Statistical inference often requires analyzing functions of numerous canonical parameters.
  • Frequentist inference typically relies on profile likelihood, which is computationally challenging for hierarchical models due to high-dimensional integration.
  • Existing methods struggle with the complexity of likelihood computation in hierarchical settings.

Purpose of the Study:

  • To develop a computationally efficient method for calculating profile likelihood for functions of parameters in general hierarchical models.
  • To provide a robust alternative to traditional methods that are hindered by integration challenges.

Main Methods:

  • The study proposes a novel computational approach using data doubling.
  • This method bypasses the need for direct high-dimensional integration of the likelihood function.
  • The technique is applicable to any specified function of the model parameters.

Main Results:

  • The data doubling method provides a simple and effective way to compute profile likelihood for hierarchical models.
  • Mathematical proofs confirm the method's validity under standard regularity conditions.
  • The approach ensures that the maximum likelihood estimator's distribution is non-singular, multivariate, and Gaussian.

Conclusions:

  • The developed computational method significantly simplifies profile likelihood inference for hierarchical models.
  • This advancement offers a practical tool for frequentist statistical analysis in complex modeling scenarios.
  • The data doubling technique enhances the tractability of statistical inference for functions of parameters in hierarchical structures.