Title: On an exact nonparametric test for class separability for the purpose of filter-type model selection
Authors: Fabian Schroeder - AIT Austrian Institute of Technology GmbH (Austria) [presenting]
Peter Filzmoser - Vienna University of Technology (Austria)
Abstract: The aim is to introduce and to discuss a statistical test based on the prediction error of a nonparametric classifier for the purpose of filter-type variable selection. This approach has several advantages. First, it naturally accounts for the operating conditions of the classification task, comprising the misclassification costs of the class distribution in the overall population. Many common filter statistics, e.g. the t-test disregard the operation conditions as well as differences in the variances between the class conditionals, which may lead to false conclusions. Secondly, the nonparametric approach guarantees that the differences in the test statistic do not only reflect the differences in the extent to which the variables satisfy the distributional assumption. It is, thus, robust with respect to deviations from the distributional assumptions, e.g. skewness or outliers. Thirdly, it is possible to obtain the exact finite sample distribution of the test statistic under the assumption of equal class conditionals. The exact significance of the classification result, as given by the p-value, is very handy since it gives an absolute criterion for the filter rather than just a relative one, which only allows ranking the variables. Furthermore it also allows adjusting the p-values for the number of tests performed.