Speaker 1: Moumita Karmakar

Title

Theoretical justification for consistent variable selection in Principal Fitted Components model

Abstract

Principal fitted component (PFC) models are a class of likelihood-based inverse regression methods that yield a so-called sufficient reduction of the random p-vector of predictors X given the response Y. Assuming that a large number of the predictors has no information about Y, we aimed to obtain an estimate of the sufficient reduction that "purges" these inactive predictors, and thus select the most useful ones. PFC-pv devised a procedure using observed significance values from the univariate fittings to yield a sparse PFC, a purged estimate of the sufficient reduction. PFC-lrt method is a novel approach for variable selection in high dimensions when the relationship between the active predictors and the response is nonlinear.  Simulation studies of both methods suggest a favorable behavior and a possible consistency of the selection of active predictors as n increases. Theoretical validation needs to be established to support the simulation results. We will discuss possible approaches to justify consistency for above two methods theoretically.