Robust Modeling Using Non-Elliptically Contoured Multivariate t Distributions

TL;DR

This paper introduces a generalized multivariate t distribution allowing different marginal degrees of freedom, enhancing modeling flexibility for heavy-tailed data, and develops Bayesian inference methods for these models.

Contribution

It extends traditional multivariate t distributions to non-elliptically contoured forms with varying marginal degrees of freedom, enabling more accurate modeling of diverse heavy-tailed data.

Findings

Models with different marginal degrees of freedom better fit heavy-tailed data.

Simulation studies show sensitivity of conclusions to marginal heavy-tailedness.

Real data examples demonstrate practical advantages of the proposed models.

Abstract

Models based on multivariate t distributions are widely applied to analyze data with heavy tails. However, all the marginal distributions of the multivariate t distributions are restricted to have the same degrees of freedom, making these models unable to describe different marginal heavy-tailedness. We generalize the traditional multivariate t distributions to non-elliptically contoured multivariate t distributions, allowing for different marginal degrees of freedom. We apply the non-elliptically contoured multivariate t distributions to three widely-used models: the Heckman selection model with different degrees of freedom for selection and outcome equations, the multivariate Robit model with different degrees of freedom for marginal responses, and the linear mixed-effects model with different degrees of freedom for random effects and within-subject errors. Based on the Normal mixture representation of our t distribution, we propose efficient Bayesian inferential procedures for the model parameters based on data augmentation and parameter expansion. We show via simulation studies and real examples that the conclusions are sensitive to the existence of different marginal heavy-tailedness.