Random projection-based response best-subset selector for ultra-high dimensional multivariate data

Abstract

In this article, we propose a random projection-based response best-subset selector to perform response variable selection in ultra-high dimensional multivariate data, where both the dimensions of response and predictor variables are substantially greater than the sample size. This method is developed by integrating the response best-subset selector and random projection technique which is applied to reduce dimensionality of predictors. Under a multivariate tail eigenvalue condition, such a random projection-based dimensionality reduction of predictors only leads to an ignorable error between the original and dimension-reduced models. A computational procedure is presented. The proposed method exhibits model consistency under some certain conditions. The efficiency and merit of the proposed method are strongly supported by extensive finite-sample simulation studies. A real breast cancer dataset spanning 22 chromosomes are analyzed to demonstrate the proposed method.