Exact nonnull distribution of Wilks' statistic: The ratio and product of independent components

JOURNAL OF MULTIVARIATE ANALYSIS

卷:102

Article

Bekker, A.¹  Roux, J. J. J.¹  Arashi, M.² 

[1] Univ Pretoria, Dept Stat, Fac Nat & Agr Sci, ZA-0002 Pretoria, South Africa

[2] Shahrood Univ Technol, Fac Math, Shahrood, Iran

关键词: Invariant polynomials;    Meijer's G-function;    Noncentral matrix variate beta type I distribution;    Product;    Ratio;    Wilks' statistic;    Zonal polynomial;   

DOI  :  10.1016/j.jmva.2010.11.005

来源: Elsevier

【 摘 要 】

The study of the noncentral matrix variate beta type distributions has been sidelined because the final expressions for the densities depend on an integral that has not been resolved in an explicit way. We derive an exact expression for the nonnull distribution of Wilks' statistic and precise expressions for the densities of the ratio and product of two independent components of matrix variates where one matrix variate has the noncentral matrix variate beta type I distribution and the other has the matrix variate beta type I distribution. We provide the expressions for the densities of the determinant of the ratio and the product of these two components. These distributions play a fundamental role in various areas of statistics, for example in the criteria proposed by Wilks. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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