Unified mean-variance feature screening for ultrahigh-dimensional regression

Feature screening is a popular and efficient statistical technique in processing ultrahigh-dimensional data. When a regression model consists both categorical and continuous predictors, a unified feature screening procedure is needed. Thus, we propose a unified mean-variance sure independence screening (UMV-SIS) for this setup. The mean-variance (MV), an effective utility to measure the dependence between two random variables, is widely used in feature screening for discriminant analysis. In this paper, we advocate using the kernel smoothing method to estimate MV between two continuous variables, thereby extending it to screen categorical and continuous predictors simultaneously. Besides the uniformity for screening, UMV-SIS is a model-free procedure without any specification of a regression model; this broadens the scope of its application. In theory, we show that the UMV-SIS procedure has the sure screening and ranking consistency properties under mild conditions. To solve some difficulties in marginal feature screening for linear model and further enhance the screening performance of our proposed method, an iterative UMV-SIS procedure is developed. The promising performances of the new method are supported by extensive numerical examples.