Hypothesis testing in finite mixture of regressions: Sparsity and model selection uncertainty
Abbas Khalili, Anand N. Vidyashankar · Canadian Journal of Statistics · 2018
Abstract Sparse finite mixture of regression models arise in several scientific applications and testing hypotheses concerning regression coefficients in such models is fundamental to data analysis. In this article, we describe an approach for hypothesis testing of regression coefficients that take into account model selection uncertainty. The proposed methods involve (i) estimating the active predictor set of the sparse model using a consistent model selector and (ii) testing hypotheses concerning the regression coefficients associated with the estimated active predictor set. The methods asymptotically control the family wise error rate at a pre‐specified nominal level, while accounting for variable selection uncertainty. Additionally, we provide examples of consistent model selectors and describe methods for finite sample improvements. Performance of the methods is also illustrated using simulations. A real data analysis is included to illustrate the applicability of the methods. The Canadian Journal of Statistics 46: 429–457; 2018 © 2018 Statistical Society of Canada