  Independence screening is a variable selection method that uses a ranking
criterion to select significant variables, particularly for statistical models
with nonpolynomial dimensionality or "large p, small n" paradigms when p can be
as large as an exponential of the sample size n. In this paper we propose a
robust rank correlation screening (RRCS) method to deal with ultra-high
dimensional data. The new procedure is based on the Kendall \tau correlation
coefficient between response and predictor variables rather than the Pearson
correlation of existing methods. The new method has four desirable features
compared with existing independence screening methods. First, the sure
independence screening property can hold only under the existence of a second
order moment of predictor variables, rather than exponential tails or
alikeness, even when the number of predictor variables grows as fast as
exponentially of the sample size. Second, it can be used to deal with
semiparametric models such as transformation regression models and single-index
models under monotonic constraint to the link function without involving
nonparametric estimation even when there are nonparametric functions in the
models. Third, the procedure can be largely used against outliers and influence
points in the observations. Last, the use of indicator functions in rank
correlation screening greatly simplifies the theoretical derivation due to the
boundedness of the resulting statistics, compared with previous studies on
variable screening. Simulations are carried out for comparisons with existing
methods and a real data example is analyzed.
