Variable selection with nonnegative garrote in additive models

Abstract

The nonnegative garrote was originally proposed by Breiman (1995) for variable selection in a multiple linear regression context. The procedure starts from the ordinary least squares estimator (OLS) and shrinks or puts some coefficients of the OLS equal to zero. In this work we consider a functional additive model and use P-splines as a basic estimation method. P-splines were introduced by Eilers and Marx (1996) as a univariate flexible smoothing technique. We therefore combine this technique with a backfitting algorithm to deal with the additive modelling. A nonnegative garrote step then takes care of the variable selection issue.