Likelihood Inference for Factor Copula Models with Asymmetric Tail Dependence.

Area of Science:

• Statistics
• Extreme Value Theory
• Copula Models

Background:

• Likelihood inference for multivariate non-Gaussian data using copulas often struggles with joint tail dependence.
• Standard models may not accurately capture extreme value behavior, particularly tail dependence strength.

Purpose of the Study:

• To propose a novel method for enhancing extreme value inferences in the presence of asymmetric tail dependence.
• To improve the assessment of joint tail dependence in multivariate non-Gaussian settings.

Main Methods:

• A Bayesian approach is proposed, incorporating a prior on tail dependence.
• Combines prior information with a potentially misspecified likelihood to form a tilted log-likelihood.
• Utilizes Bayesian computing or numerical optimization to estimate posterior modes and Hessians.

Main Results:

• The proposed method improves inferences for joint lower and upper tails.
• Effectively addresses limitations of standard likelihood methods in capturing tail dependence.
• Provides a robust framework for extreme value analysis with asymmetric tails.

Conclusions:

• The combined prior and likelihood approach offers a powerful tool for accurate extreme value inference.
• This method is particularly beneficial when asymmetric tail dependence is suspected.
• Enhances the reliability of assessing tail dependence strength in complex multivariate data.