Screening and Clustering of Sparse Regressions with Finite Non-Gaussian Mixtures

This article proposes a method to address the problem that can arise when covariates

in a regression setting are not Gaussian, which may give rise to approximately mixture-distributed

errors, or when a true mixture of regressions produced the data. The method begins with non-

Gaussian mixture-based marginal variable screening, followed by fitting a full but relatively smaller

mixture regression model to the selected data with help of a new penalization scheme. Under certain

regularity conditions, the new screening procedure is shown to possess a sure screening property

even when the population is heterogeneous. We further prove that there exists an elbow-point in

the associated scree plot which results in a consistent estimator of the set of active covariates in

the model. By simulations, we demonstrate that the new procedure can substantially improve the

performance of the existing procedures in the content of variable screening and data clustering. By

applying the proposed procedure to motif data analysis in molecular biology, we demonstrate that

the new method holds promise in practice.