Extensão do teste de normalidade de shapiro-francia para o caso multivariado
The present work emphasizes the importance of multivariate normality test, since the assumption that a set of multivariate data come from a multivariate normal distribution is central in many multivariate statistical techniques. If this assumption is not satisfied, the results of statistical analysi...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2009 |
| País: | Brasil |
| Institución: | Universidade Federal de Lavras (UFLA) |
| Repositorio: | Repositório Institucional da UFLA |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufla.br:1/4404 |
| Acceso en línea: | https://repositorio.ufla.br/handle/1/4404 |
| Access Level: | acceso abierto |
| Palabra clave: | CNPQ_NÃO_INFORMADO Simulação monte carlo Shapiro-wilk Teste de normalidade multivariado Shapiro-francia Monte carlo simulation Multivariate normality test |
| Sumario: | The present work emphasizes the importance of multivariate normality test, since the assumption that a set of multivariate data come from a multivariate normal distribution is central in many multivariate statistical techniques. If this assumption is not satisfied, the results of statistical analysis becomes unreliable. Shapiro & Francia (1972) proposed an alternative test of Shapiro & Wilk (1965) univariate which shows the same properties related to the performance of the Shapiro andWilk´ test. The great advantage the Shapiro and Francia´s univariate normality test is simplicity of obtaining estimates of the coefficients associated with the statistics of order a, for the same quantities of the Shapiro-Wilk test. There is no papers reporting implementation of Royston multivariate normality test (Royston, 1983b, 1993) in any statistical analysis system. One reason is the difficulty in its implementation. For this reason this research proposed the multivariate extension of the univariate normality Shapiro-Francia´s test (Shapiro & Francia, 1972). The performance of tests was evaluating the type I error rates and power using Monte Carlo simulation. The Shapiro-Francia univariate normality test was extended to the multivariate case successfully, controlled the type I error and was considered equivalent to the multivariate Shapiro-Wilk´s normality test. The power of the new test was in general equal and greater than the power of the multivariate Shapiro-Wilk´s normality test. There is no test uniformly superior in all cases. The new Shapiro and Francia´s multivariate normality test is recommended in applications that require evaluating for multivariate normality. |
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