Analise Discriminante Novos Metodos Robustos de Estimacao

This thesis was developed bearing in mind two main purposes: first, the assessment, from a robust viewpoint, of the various discriminant analysis procedures; second, the development of robust alternative and competitive methodology. The first three chapters are related to the first purpose and the remaining to the second. Chapter 1 presents several examples and introduces the formulation, basic notation and a description of decision criteria. Chapter 2 considers special important cases of the application of those criteria to the simulation of known distributions. Chapter 3 introduces the main estimation procedures, and compares their advantages in regard to robustness. In the second part only the linear discriminant function for two groups - a particular case which is central in Discriminant Analysis studies - is considered. Chapter 4 proposes two new approaches to robust estimation of that function. The first relies on reweighted estimators, with weights determined from the influence function, in such a way that the potentially most inffluent observations receive a small weight. The second approach is based on an adaptation of projection-pursuit ideas to the problem of Discriminant Analysis. Chapter 5 presents the results of a simulation study designed to compare the new methods with the main competitors. Those results show a very good behaviour of the new procedures not only in terms of robustness but also in efficiency. In Chapter 6 the problem of variable selection is briefly discussed. Finally, Chapter 7 states the main conclusions and discusses future workAvailable from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1200 Lisboa / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga