External Seminar: David Rossell (University of Warwick)

[Statistics & Probability Seminar]

On robust inference based on two-piece distributions

A main challenge in high-dimensional inference is to enforce sparsity adequately. Because of theoretical and computational difficulties in non-standard settings, most research efforts have been focused on the Normal distribution. While convenient, the Normal is not flexible enough to capture asymmetric or heavy-tailed data-generating mechanisms and it is well-known to be particularly sensitive to these situations where influential observations are likely to occur. We consider an extension of the Normal framework via two-piece distributions (TPD). TPDs add flexibility and are more robust, but they enjoy interesting properties that make them analytically and comptutationally tractable. As a first example we consider a linear regression framework with flexible unimodel errors, where we show that the corresponding log-likelihoods are concave (computationally tractable) and asymptotic characterizations are possible (analytically tractable). As a second example we consider non-normal mixture models, where TPDs facilitate obtaining more robust and interpretable clusters.