Optimal rank-based tests for homogeneity of scatter

• 成果类型: Article
• 署名作者: Hallin, Marc; Paindaveine, Davy
• 署名单位: Universite Libre de Bruxelles; Universite Libre de Bruxelles
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS508
• 发表日期: 2008
• 页码: 1261-1298
• 关键词: Covariance matrices; Adaptive estimation; m-functionals; MULTIVARIATE; shape; bootstrap; distributions; EFFICIENCY; variances; inference

摘要

We propose a class of locally and asymptotically optimal tests, based on multivariate ranks and signs for the homogeneity of scatter matrices in M. elliptical populations. Contrary to the existing parametric procedures, these tests remain valid without any moment assumptions, and thus are perfectly robust against heavy-tailed distributions (validity robustness). Nevertheless, they reach semiparametric efficiency bounds at correctly specified elliptical densities and maintain high powers under all (efficiency robustness). In particular, their normal-score version outperforms traditional Gaussian likelihood ratio tests and their pseudo-Gaussian robustifications under a very broad range of non-Gaussian densities including, for instance, all multivariate Student and power-exponential distributions.