Robust Sure Independence Screening for Ultrahigh Dimensional Models

Independent screening is a variable selection method that uses a ranking criterion to select significant variables particularly for the statistical model with NP-dimensionality or "large $p$, small $n$" paradigms when $p$ can even be as large as exponential of the sample size $n$. However, it requires exponential tails of variables and has not yet been applied to semiparametric models. In this paper, we propose a rank correlation screening (RCS) to deal with ultra-high dimensional data. The new procedure possesses the sure independence screening property without the assumption on exponential tails of variables even when the number of predictor variables grows as fast as exponential of the sample size. Furthermore, the proposed method can be used to deal with semiparametric models such as transformation regression models and single-index models. The estimation efficiency of our method is demonstrated through extensive comparisons with other methods by simulation studies.