Pruning a sufficient dimension reduction with a p-value guided hard-thresholding. Issue 2 (3rd March 2016)

• Record Type: Journal Article
• Authors: Adragni, Kofi P.; Xi, Mingyu
• Is Part Of: Statistics. Volume 50:Issue 2(2016)
• Page Start: 254
• Page End: 270
• Publication Date: 2016-03-03
• Subjects: dimension reduction -- principal fitted component -- sparsity -- variable selection; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2015.1050019
• Languages: English
• ISSNs: 0233-1888

Abstract

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 irrelevant predictors, and thus, select the most useful ones. We devised a procedure using observed significance values from the univariate fittings to yield a sparse PFC, a purged estimate of the sufficient reduction. The performance of the method is compared to that of penalized forward linear regression models for variable selection in high-dimensional settings.