  Datasets containing both categorical and continuous variables are frequently
encountered in many areas, and with the rapid development of modern measurement
technologies, the dimensions of these variables can be very high. Despite the
recent progress made in modelling high-dimensional data for continuous
variables, there is a scarcity of methods that can deal with a mixed set of
variables. To fill this gap, this paper develops a novel approach for
classifying high-dimensional observations with mixed variables. Our framework
builds on a location model, in which the distributions of the continuous
variables conditional on categorical ones are assumed Gaussian. We overcome the
challenge of having to split data into exponentially many cells, or
combinations of the categorical variables, by kernel smoothing, and provide new
perspectives for its bandwidth choice to ensure an analogue of Bochner's Lemma,
which is different to the usual bias-variance tradeoff. We show that the two
sets of parameters in our model can be separately estimated and provide
penalized likelihood for their estimation. Results on the estimation accuracy
and the misclassification rates are established, and the competitive
performance of the proposed classifier is illustrated by extensive simulation
and real data studies.
