Identification in Bayesian Estimation of the Skewness Matrix in a Multivariate Skew-Elliptical Distribution

08/09/2021
by   Sakae Oya, et al.
0

Harvey et al. (2010) extended the Bayesian estimation method by Sahu et al. (2003) to a multivariate skew-elliptical distribution with a general skewness matrix, and applied it to Bayesian portfolio optimization with higher moments. Although their method is epochal in the sense that it can handle the skewness dependency among asset returns and incorporate higher moments into portfolio optimization, it cannot identify all elements in the skewness matrix due to label switching in the Gibbs sampler. To deal with this identification issue, we propose to modify their sampling algorithm by imposing a positive lower-triangular constraint on the skewness matrix of the multivariate skew- elliptical distribution and improved interpretability. Furthermore, we propose a Bayesian sparse estimation of the skewness matrix with the horseshoe prior to further improve the accuracy. In the simulation study, we demonstrate that the proposed method with the identification constraint can successfully estimate the true structure of the skewness dependency while the existing method suffers from the identification issue.

READ FULL TEXT

page 11

page 12

page 13

research
06/18/2019

Blending the New Statistics with Mixture Modeling -- A ROPE-based single-block Gibbs sampler for Bayesian t-tests

Testing the difference of means between two groups is one of the oldest ...
research
04/25/2015

A Prior Distribution over Directed Acyclic Graphs for Sparse Bayesian Networks

The main contribution of this article is a new prior distribution over d...
research
01/14/2020

An Efficient Gibbs Sampling Algorithm for Bayesian Graphical LASSO Models with the Positive Definite Constraint on the Precision Matrix

Wang (2012) proposed a novel Gibbs sampling algorithm for Bayesian analy...
research
12/17/2021

Moments and random number generation for the truncated elliptical family of distributions

This paper proposes an algorithm to generate random numbers from any mem...
research
04/14/2020

Extensions of Random Orthogonal Matrix Simulation for Targetting Kollo Skewness

Modelling multivariate systems is important for many applications in eng...
research
07/02/2021

Reconsidering Dependency Networks from an Information Geometry Perspective

Dependency networks (Heckerman et al., 2000) are potential probabilistic...
research
08/18/2020

Moment Multicalibration for Uncertainty Estimation

We show how to achieve the notion of "multicalibration" from Hébert-John...

Please sign up or login with your details

Forgot password? Click here to reset