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Information bounds for Gaussian copulas.

Peter D Hoff1, Xiaoyue Niu2, Jon A Wellner1

  • 1Professor of Statistics and Biostatistics University of Washington Seattle, WA 98195-4322.

Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability
|October 15, 2014
PubMed
Summary
This summary is machine-generated.

Rank-based estimators are effective for semiparametric copula estimation, focusing on dependence structures. This study establishes their asymptotic properties for Gaussian copula models, showing equivalence to parametric methods.

Keywords:
copula modellocal asymptotic normalitymarginal likelihoodmultivariate rank statisticsrank likelihoodtransformation model

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Area of Science:

  • Statistics
  • Multivariate Data Analysis
  • Copula Theory

Background:

  • Copula parameters are crucial for understanding multivariate data dependence.
  • Rank-based estimators offer a semiparametric approach to copula estimation, invariant to marginal distributions.
  • Analyzing the rank likelihood is key to determining asymptotic information bounds.

Purpose of the Study:

  • To derive the limiting normal distributions of the rank likelihood for Gaussian copula models.
  • To investigate these distributions for both structured and unstructured correlation matrices.
  • To compare the asymptotic properties of rank-based estimators with parametric approaches.

Main Methods:

  • Asymptotic analysis of the rank likelihood function.
  • Derivation of limiting normal distributions for rank likelihood ratios.
  • Consideration of Gaussian copula models with various correlation structures.

Main Results:

  • The limiting distribution of the rank likelihood ratio for Gaussian copulas matches that of a parametric likelihood ratio.
  • This holds true for both structured (e.g., exchangeable, circular) and unstructured correlation matrices.
  • Semiparametric information bounds for rank-based estimators are equivalent to parametric bounds.

Conclusions:

  • Rank-based semiparametric copula estimation achieves the same information bounds as parametric methods.
  • Multivariate normal distributions are identified as least favorable in this context.
  • The findings support the use of rank-based methods for robust dependence analysis in Gaussian copulas.