Computationally Efficient Tests for Multivariate Skew Normality

作     者：Gonzalez-Estrada, Elizabeth 

作者机构：Colegio Postgrad Programa Estadist & Ciencia Datos Carr Mexico Texcoco Km 36-5 Mexico City 56230 Mexico 

出 版 物：《JOURNAL OF STATISTICAL THEORY AND PRACTICE》 (J. Stat. Theory Pract.)

年 卷 期：2025年第19卷第3期

页      面：1-22页

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Shapiro-Wilk test for normality Goodness-of-fit Test for the gamma distribution Data transformations Type I error probability 

摘      要：This manuscript addresses the problem of testing the multivariate skew normal distribution hypothesis when parameters are unknown. Data transformations to observations with approximately univariate normal distribution are employed to propose four computationally efficient tests for this composite hypothesis. The Shapiro-Wilk test is applied for assessing the normality of the transformed data. Existing normal approximations are used for computing the critical constants of this test, avoiding the use of expensive resampling techniques like parametric bootstrap. The size and power properties of these procedures are studied by means of Monte Carlo simulation, including different parameter configurations under the null and alternative hypotheses. Two of the proposed procedures have pretty good control of the type I error probability under the considered settings. Real data examples are included to illustrate the utility of the tests.