A new multivariate t distribution with variant tail weights and its application in robust regression analysis

Area of Science:

• Statistics
• Probability Theory
• Econometrics

Background:

• Classical multivariate t-distributions offer limited flexibility in modeling marginal tail weights.
• Existing models struggle to accommodate heterogeneous tail behaviors in multivariate data.

Purpose of the Study:

• To propose a novel multivariate t-distribution with component-wise degrees of freedom.
• To enhance flexibility in multivariate data modeling and regression analysis.
• To address limitations of classical multivariate t-distributions.

Main Methods:

• Development of a new multivariate t-distribution allowing different degrees of freedom for each component.
• Exploration of key distributional properties and statistical methodologies.
• Extension of the distribution to model error terms in regression analysis.

Main Results:

• The proposed distribution offers greater flexibility than the classical multivariate t-distribution.
• It can incorporate multivariate normal components and products of independent t-distributions.
• Simulation studies and real data analyses demonstrate its effectiveness.

Conclusions:

• The new multivariate t-distribution provides a more adaptable framework for modeling data with varying tail characteristics.
• Its application in regression models improves the capture of data features.
• The methodology is validated through empirical studies.