Likelihood Ratio Test For The Multivariate Normal Generalized Variance
An interesting measure of variability in multivariate populations is the determinant of the covariance matrix Σp×p, denoted as |Σ|, commonly referred to as generalized variance. This measure succinctly captures the dispersion of a multivariate population into a single value, while accounting for int...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | Brasil |
| Institución: | Universidade Federal de Lavras (UFLA) |
| Repositorio: | Brazilian Journal of Biometrics |
| Idioma: | inglés |
| OAI Identifier: | oai:biometria.ufla.br:article/711 |
| Acceso en línea: | https://biometria.ufla.br/index.php/BBJ/article/view/711 |
| Access Level: | acceso abierto |
| Palabra clave: | Monte Carlo Standardized generalized variance Variability measure |
| Sumario: | An interesting measure of variability in multivariate populations is the determinant of the covariance matrix Σp×p, denoted as |Σ|, commonly referred to as generalized variance. This measure succinctly captures the dispersion of a multivariate population into a single value, while accounting for inter-variable dependencies. Consequently, it finds applications across various domains concerned with assessing dispersion within multivariate populations of interest. In this study, we introduce a likelihood ratio test for the generalized variance of multivariate normal distributions, accompanied by a theoretical exposition on the distribution theory of sample generalized variances. We propose both the Likelihood Ratio Test (LRT) and the Bartlett-Corrected Likelihood Ratio Test (BCLRT) for assessing the hypothesis that the generalized variance equals a parameter η, where η ∈ R. The development of these tests is purely theoretical. Our recommendation is to employ the BCLRT test primarily in scenarios where p = 2, particularly when n > 30. As for the LRT test, we suggest its application in cases where p = 2 or p = 3, provided that n > 30, and for p = 5 when n > 50. |
|---|