Statistics across Campuses: Linh Nghiem -- Estimation of Graphical Models for a class of Multivariate Skew-Symmetric Distributions

Title: Estimation of Graphical Models for a class of Multivariate Skew-Symmetric
Distributions 

Date: 26 June 2020, Friday 

Time: 4pm 

Speaker: Dr Linh Nghiem (ANU) 

Abstract: 

We consider the problem of estimating graphical models for data generated from a class
of multivariate skew symmetric distributions, which can be used to model multivariate
data with both moderate skewness and heavy tails.  Conditional independence between any
component requires both the corresponding element of the inverse covariance matrix and
the product of the two corresponding components in the shape vector to be zero.
Utilizing new properties of the conditional expectation in this class of distributions,
we propose a novel two-step nodewise approach to estimate the graphical model.  For each
nodewise regression, we first fit a linear model using least squares, and then fit a
one-component projection pursuit regression on the residual obtained from the first
step.  The graph is estimated by thresholding an appropriate quantity from all the
nodewise regressions.  We prove consistency of the estimated graph in a setting that
allows both the sample size and the number of variables to diverge.  Simulation results
show the superior performance of the new method in estimating the true graphical model
compared to common methods that are used for estimating the Gaussian graphical model.
Finally, the new method is applied on a dataset regarding the physicochemical properties
of wine.  

Link: https://au.bbcollab.com/guest/fcf219c74ac743e89565a9e6e8d349a9