Localized Regression

The main problem with localized discriminant techniques is the
curse of dimensionality, which seems to restrict their use to the
case of few variables. This restriction does not hold if
localization is combined with a reduction of dimension. In
particular it is shown that localization yields powerful
classifiers even in higher dimensions if localization is combined
with locally adaptive selection of predictors. A robust localized
logistic regression (LLR) method is developed for which all tuning
parameters are chosen data¡adaptively. In an extended simulation
study we evaluate the potential of the proposed procedure for
various types of data and compare it to other classification
procedures. In addition we demonstrate that automatic choice of
localization, predictor selection and penalty parameters based on
cross validation is working well. Finally the method is applied to
real data sets and its real world performance is compared to
alternative procedures.