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On specification tests for composite likelihood inference.

Jing Huang1, Yang Ning2, Nancy Reid3

  • 1Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A.

Biometrika
|June 28, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces new specification tests for composite likelihood inference, ensuring valid statistical analysis even with complex data structures. These tests help confirm model accuracy, enhancing the reliability of research findings.

Keywords:
Bartlett identityInformation matrixMisspecification testModel specification

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Area of Science:

  • Statistics
  • Statistical Inference
  • Computational Statistics

Background:

  • Composite likelihood functions are widely used for statistical inference, particularly with complex data structures.
  • While offering robustness, composite likelihood inference is only valid if underlying models are correctly specified.
  • Model misspecification can lead to invalid inferences, necessitating robust diagnostic tools.

Purpose of the Study:

  • To propose a general class of specification tests for composite likelihood inference.
  • To develop methods for validating the correctness of component models within composite likelihood frameworks.
  • To ensure the reliability and accuracy of statistical inferences derived from composite likelihoods.

Main Methods:

  • Development of specification tests based on the second Bartlett identity for composite likelihood components.
  • Construction of test statistics measuring the discrepancy between the composite information matrix and the sensitivity matrix.
  • Derivation of limiting distributions for test statistics under null and local alternative hypotheses.

Main Results:

  • A novel class of specification tests for composite likelihood inference is proposed.
  • The theoretical properties, including limiting distributions, of these tests are established.
  • The finite-sample performance of the proposed tests is evaluated through simulations and examples.

Conclusions:

  • The proposed specification tests provide a valid framework for assessing the correctness of composite likelihood models.
  • These tests are crucial for ensuring the robustness and reliability of statistical inference in complex data scenarios.
  • The methodology offers a valuable tool for researchers utilizing composite likelihood methods.