Some notes on robust sure independence screening

Sure independence screening (SIS) proposed by Fan and Lv [4 J. Fan and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Amer. Statist. Assoc. 96 (2001), pp. 1348–1360. doi: 10.1198/016214501753382273[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] uses marginal correlations to select important variables, and has proven to be an efficient method for ultrahigh-dimensional linear models. This paper provides two robust versions of SIS against outliers. The two methods, respectively, replace the sample correlation in SIS with two robust measures, and screen variables by ranking them. Like SIS, the proposed methods are simple and fast. In addition, they are highly robust against a substantial fraction of outliers in the data. These features make them applicable to large datasets which may contain outliers. Simulation results are presented to show their effectiveness.