Uniform simulation of symmetric positive definite matrices, with applications to evaluating classifiers.

Abstract

In this dissertation a systematic approach for evaluating statistical techniques over a broad range of plausible correlation structures is introduced. The idea is to generate covariance matrices from a certain distribution and evaluate statistical techniques over this distribution or its generalizations. The methods for generating SPD matrices uniformly from correlation cone, covariance cone with a trace bound and covariance cone with an eigenvalue bound are developed. Three generalizations of correlation distribution are introduced for describing the range of correlation structures presented by many different application domains. The evaluation of statistical techniques using this approach is illustrated by comparing Fisher's Rule and Independence Rule over uniform correlation distribution and its generalizations. Using simulation results, plots are constructed for choosing a classifier between these two rules based on training data sets only. The use of these plots is illustrated with real data sets.