Non-parametric smoothing of the location model in mixed variable discrimination

The location model is a familiar basis for discriminant analysis of mixtures of categorical and continuous variables. Its usual implementation involves second-order smoothing, using multivariate regression for the continuous variables and log-linear models for the categorical variables. In spite of the smoothing, these procedures still require many parameters to be estimated and this in turn restricts the categorical variables to a small number if implementation is to be feasible. In this paper we propose non-parametric smoothing procedures for both parts of the model. The number of parameters to be estimated is dramatically reduced and the range of applicability thereby greatly increased. The methods are illustrated on several data sets, and the performances are compared with a range of other popular discrimination techniques. The proposed method compares very favourably with all its competitors.