A sequential test for variable selection in high dimensional complex data

作者：Adragni Kofi P^*; Karmakar Moumita

来源：Computational Statistics & Data Analysis, 2015, 81: 107-120.

DOI：10.1016/j.csda.2014.07.016

• Inverse regression
• Dimension reduction
• Principal components
• Variable selection
• Variable screening
• High dimensionality
• Data analysis

Given a high dimensional p-vector of continuous predictors X and a univariate response Y, principal fitted components (PFC) provide a sufficient reduction of X that retains all regression information about Y in X while reducing the dimensionality. The reduction is a set of linear combinations of all the p predictors, where with the use of a flexible set of basis functions, predictors related to Y via complex, nonlinear relationship can be detected. In the presence of possibly large number of irrelevant predictors, the accuracy of the sufficient reduction is hindered. The proposed method adapts a sequential test to the PFC to obtain a "pruned" sufficient reduction that shed off the irrelevant predictors. The sequential test is based on the likelihood ratio which expression is derived under different covariance structures of X vertical bar Y. The resulting reduction has an improved accuracy and also allows the identification of the relevant variables.

• 出版日期2015-1