Screening and Selection Methods in High-Dimensional Linear Regression Model
Shinpei Imori, Shota Katayama and Hirofumi Wakaki
Abstract
In the present paper, we propose a new variable selection procedure for a high-dimensional
linear model from two perspectives of the true and risk minimizing model selection. The
proposed method consists of two factors: screening and selection. Both parts are based on
the residual sum of squares, which can be easily understood. Our objective is to select a
model consisting of indices of all nonzero regression coefficients, which is known as the true
model when the true mean structure is included in the full model. Moreover, it minimizes the
risk function under a restriction of explanatory variables. Even when the space of the target
model is large, our selection method is consistent under mild conditions, i.e., the selection
probability of the objective model goes to 1. Additionally, we reveal that consistency is
retained when the true mean structure cannot be constructed from all available explanatory
variables. Through simulation studies, we illustrate that our screening and selection methods
are more effective than previous methods in various situations.
Preprint
http://www.math.sci.hiroshima-u.ac.jp/stat/TR/TR14/TR14-01.pdf
