A0443
Title: Tests for the multivariate skew-normal distribution based on data transformations
Authors: Aurora Monter-Pozos - Colegio de Postgraduados (Mexico) [presenting]
Elizabeth Gonzalez-Estrada - Colegio de Postgraduados (Mexico)
Abstract: The parametric statistical inference relies on the assumption that the data are a random sample from a population that has a given probability distribution. This kind of inference is valid only if the probability distribution used really explains the probabilistic behaviour of the data. A probability distribution that has gained importance in the last decades is the multivariate skew normal (MSN) distribution, which extends the normal one by incorporating a shape parameter. It provides probability models for datasets showing moderate degrees of skewness. Goodness-of-fit tests for the MSN distribution are proposed based on the canonical transformation and an additional transformation to multivariate normality. Then, the problem of testing the null hypothesis that a random sample follows an MSN distribution with unknown parameters is reduced to testing that the sample comes from a multivariate Gaussian distribution. Simulation results show that the proposed tests have desirable properties and are competitive against existing tests for the same problem. A real data set is analyzed in order to illustrate the usefulness of the tests.
