Penalized estimation in finite mixture of ultra-high dimensional regression models

In this paper, we propose a penalized estimation method for finite mixture of ultra-high dimensional regression models. A two-step procedure is explored. Firstly, we conduct order selection with the number of components unknown. Then variable selection is applied to ultra-high dimensional regression models. A specific EM algorithm is designed to maximize penalized log-likelihood function. We demonstrate our method by numerical simulations which performs well. Further, an empirical study of return on equity (ROE) prediction is shown to consolidate our methodology.