Variable Selection in Nonparametric Classification Via Measurement Error Model Selection Likelihoods

Using the relationships among ridge regression, LASSO estimation, and measurement error attenuation as motivation, a new measurement-error-model-based approach to variable selection is developed. After describing the approach in the familiar context of linear regression, we apply it to the problem of variable selection in nonparametric classification, resulting in a new kernel-based classifier with LASSO-like shrinkage and variable-selection properties. Finite-sample performance of the new classification method is studied via simulation and real data examples, and consistency of the method is studied theoretically. Supplementary materials for the article are available online.