Variable Selection Procedures in Linear Regression Models with Screening Consistency Property

There are two fundamental goals in statistical learning： identifying relevant predictors and ensuring high prediction accuracy. The first goal, by means of variable selection, is of particular importance when the true underlying model has a sparse representation. Discovering relevant predictors can enhance the performance of the prediction for the fitted model. Usually an estimate is considered desirable if it is consistent in terms of both coefficient estimate and variable selection. Hence, before we try to estimate the regression coefficients β , it is preferable that we have a set of useful predictors m hand. The emphasis of our task in this paper is to propose a method, in the aim of identifying relevant predictors to ensure screening consistency in variable selection. The primary interest is on Orthogonal Matching Pursuit（OMP）.