PhD Thesis In: cienciavitae
MÉTODOS ROBUSTOS EM ANÁLISE DE CORRELAÇÕES CANÓNICAS
— 2002
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June 2002
Abstract
Canonical correlation analysis is the multivariate method appropriate to study the associations that may exist between two groups of variables. Some of the most important multivariate methods are special cases of canonical correlation analysis of this method is its capacity to reduce to a few dimensions the relevant associations between two groups of variables. Although the classical estimation methods are optimal, when certain distributional hypotheses are true, their estimates can be strongly affected by the presence of atypical observations. These observations are frequent in real data and are difficult to detect, especially in multivariate data sets requiring a multivariate method of analysis, like canonical correlation analysis. Robust methods can correct these limitations. In this study, an extended review of the most relevant classical results (Chapter 2) and robust results (Chapter 3) about the canonical correlation model is presented. Three new robust estimation methods are proposed. the first one is based on M-estimators (Chapter 4) where the weights depend on the theoretical influence functions of the canonical coefficients. The second robust method of estimation is based on the projection pursuit method (Chapter 5) and the third one relies on partial least squares estimators (chapter 7). This last method is developed for the first pair of canonical variables and their canonical correlation only. The proposed methods are compared between themselves, and also with robust methods based on robust covariance matrices and with the classical method (Chapter 6). A simulation study was developed to perform these comparisons. The work ends with a short description of the most relevant results achieved and a list of new problems that will be the objective of future studies (Chapter 8).
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Degree Name
Ph.D. in Mathematics
Fields of Science and Technology (FOS)
mathematics - Mathematics
Publication language (ISO code)
por - Portuguese
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