Proposta de um teste exato para avaliar a normalidade multivariada baseado em uma transformação t de Student

Detalhes bibliográficos
Ano de defesa: 2016
Autor(a) principal: Melo, Janaína Marques de
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de Lavras
Programa de Pós-graduação em Estatística e Experimentação Agropecuária
UFLA
brasil
Departamento de Ciências Exatas
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://repositorio.ufla.br/jspui/handle/1/10807
Resumo: The normal distribution is one of the most important continuous probability distribution. This distribution describe several phenomena and has great hole in inferential statistics. It is noteworthy that the normality directly influences the quality and reliability of scientific research since violations of assumption can lead to incorrect results and conclusions. The same is expected for multivariate inferences. A simple manner, however subjective, to verify the univariate or multivariate normality is through quantile-quantile plots (Q-Q plots). Furthermore, the Q-Q plots are efficient tools for the visualization of outliers. A disadvantage of the classical Q-Q plot is that the quantiles are only asymptotically identically distributed, but they are not independent. This fact compromises the efficiency of the Q-Q plot or any test based on the use of the observed distance quantiles. The objective of this study is to propose an accurate test and validate its performance by Monte Carlo simulation and also provide a Q-Q plot to detect further evidence of violation of multivariate normality in $ p $ dimensions. This Q-Q plot originates from a characterization of the multivariate normal distribution made by Yang et al. (1996) based on the spherical distribution properties (Fang et al., 1990). The R program version 3.1.0 was used to build this Q-Q plot normality test and to perform the validation of its performance by Monte Carlo simulations. The Monte Carlo simulation results showed that the proposed test successful controls the type I error rates being accurate, but shows lower power than any other multivariate normality test.