Title: A sure independence screening procedure for ultra-high dimensional partially linear additive models,
Abstract: We introduce a two-step procedure, in the context of ultra-high dimensional
additive models, which aims to reduce the size of covariates vector and
distinguish linear and nonlinear effects among nonzero components. Our proposed
screening procedure, in the first step, is constructed based on the concept of
cumulative distribution function and conditional expectation of response in the
framework of marginal correlation. B-splines and empirical distribution
functions are used to estimate the two above measures. The sure property of
this procedure is also established. In the second step, a double penalization
based procedure is applied to identify nonzero and linear components,
simultaneously. The performance of the designed method is examined by several
test functions to show its capabilities against competitor methods when errors
distribution are varied. Simulation studies imply that the proposed screening
procedure can be applied to the ultra-high dimensional data and well detect the
in uential covariates. It is also demonstrate the superiority in comparison
with the existing methods. This method is also applied to identify most in
uential genes for overexpression of a G protein-coupled receptor in mice.