An Edgeworth-type Expansion of the Distribution of a Likelihood-based Classifier for Single Time-point Measurements and Growth Curves

Abstract

This thesis focuses on approximating misclassification errors of likelihood-based classifiers considering two cases. The first case assumes the allocation of a new observation into two normal populations. The second case classifies repeated measurements using the growth curve model, considering the fact that the new observation might not belong to any of the two predetermined populations but to an unknown population. In this thesis, likelihood-based approaches were used to derive classification rules used to allocate a new observation in any of the two predefined normally distributed populations. Moreover, a two-step likelihood-based classification of growth curves is studied from which the distribution of a new observation is either drawn from any of the two predetermined populations or from an unknown population. Furthermore, moments of the classifiers were calculated and utilized to approximate the distribution of the proposed classifiers through an Edgeworth-type expansion. In addition, probabilities of misclassifications for the above-mentioned classifiers were estimated.