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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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Dependence calibration in conditional copulas: a nonparametric approach.

Elif F Acar1, Radu V Craiu, Fang Yao

  • 1Department of Statistics, University of Toronto, Toronto, Ontario M5S 3G3, Canada. elif@utstat.toronto.edu

Biometrics
|August 25, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a new conditional copula model to analyze how the dependence between random variables changes with covariates. The method uses local likelihood for estimation and offers a novel way to select the best copula family for data.

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Area of Science:

  • Statistics
  • Probability Theory
  • Econometrics

Background:

  • Dependence between random variables is fundamental in statistics.
  • The strength of this dependence often varies based on observed covariates.
  • Existing methods may not fully capture covariate-dependent dependence structures.

Purpose of the Study:

  • To develop a statistical framework for inferring covariate-dependent dependence.
  • To propose a conditional copula model where dependence parameters vary with covariates.
  • To introduce a novel copula selection method.

Main Methods:

  • Utilizing a conditional copula model with a parametric copula family.
  • Employing a nonparametric local likelihood approach to estimate the covariate-dependence relationship.
  • Developing a copula selection criterion based on cross-validated prediction errors.

Main Results:

  • Derivation of asymptotic bias and variance for the local polynomial estimator.
  • Methodology for constructing pointwise confidence intervals.
  • Demonstration of the method's finite-sample performance via simulations.

Conclusions:

  • The proposed conditional copula model effectively captures varying dependence structures.
  • The local likelihood approach provides a robust estimation method.
  • The cross-validation-based selection criterion aids in choosing appropriate copula families.