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Omnibus tests for multivariate normality based on Mardia's skewness and kurtosis using normalizing transformation
- Authors
- Kim, Namhyun
- Issue Date
- Sep-2020
- Publisher
- KOREAN STATISTICAL SOC
- Keywords
- goodness-of-fit test; Mardia' s kurtosis; Mardia' s skewness; multivariate normality; power comparison
- Citation
- COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS, v.27, no.5, pp.501 - 510
- Volume
- 27
- Number
- 5
- Start Page
- 501
- End Page
- 510
- ISSN
- 2287-7843
- Abstract
- Mardia (Biometrika, 57, 519-530, 1970) defined measures of multivariate skewness and kurtosis. Based on these measures, omnibus test statistics of multivariate normality are proposed using normalizing transformations. The transformations we consider are normal approximation and a Wilson-Hilferty transformation. The normalizing transformation proposed by Enomoto et al. (Communications in Statistics-Simulation and Computation, 49, 684-698, 2019) for the Mardia's kurtosis is also considered. A comparison of power is conducted by a simulation study. As a result, sum of squares of the normal approximation to the Mardia's skewness and the Enomoto's normalizing transformation to the Mardia's kurtosis seems to have relatively good power over the alternatives that are considered.
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Related Researcher
- Kim, Nam hyun
- Engineering (Applied Science)