A sequential test for variable selection in high dimensional complex data

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|Y. The resulting reduction has an improved accuracy and also allows the identification of the relevant variables.