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 paper are available online.
Keywords: Attenuation; Bayes rule; Binary regression; Convolution; Discriminant analysis; Kernel discriminant analysis; LASSO; Linear regression; Maximum likelihood rule; Model selection; Ridge regression.