# Likelihood Inference for Factor Copula Models with Asymmetric Tail Dependence

## TL;DR

This paper introduces a method to improve tail dependence inference in non-Gaussian multivariate data using a combination of prior information and likelihood.

## Contribution

A novel approach to enhance extreme value inferences with asymmetric tail dependence using a tilted log-likelihood.

## Key findings

- Combining prior and likelihood improves joint tail inference.
- Bayesian computing or numerical optimization can be used with the tilted log-likelihood.
- The method addresses misspecification in the likelihood for better tail dependence assessment.

## Abstract

For multivariate non-Gaussian involving copulas, likelihood inference is dominated by the data in the middle, and fitted models might not be very good for joint tail inference, such as assessing the strength of tail dependence. When preliminary data and likelihood analysis suggest asymmetric tail dependence, a method is proposed to improve extreme value inferences based on the joint lower and upper tails. A prior that uses previous information on tail dependence can be used in combination with the likelihood. With the combination of the prior and the likelihood (which in practice has some degree of misspecification) to obtain a tilted log-likelihood, inferences with suitably transformed parameters can be based on Bayesian computing methods or with numerical optimization of the tilted log-likelihood to obtain the posterior mode and Hessian at this mode.