Near-exact Distributions for the Likelihood Ratio Statistic used to Test the Reality of a Covariance Matrix

被引：0

作者：

Grilo, Luis M. ^{[1
]}

Coelho, Carlos A. ^{[1
]}

机构：

[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Unidade Dept Matemat & Fis, Inst Politecn Tomar, P-1200 Lisbon, Portugal

来源：

11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013, PTS 1 AND 2 (ICNAAM 2013) | 2013年 / 1558卷

关键词：

Beta distribution; Characteristic function; Complex Normal distribution; ComplexWishart distribution; Generalized Near-Integer Gamma distribution; Mixtures; COMPLEX GAUSSIAN DISTRIBUTION; INTEGER GAMMA-DISTRIBUTION; BETA RANDOM-VARIABLES; EXACT APPROXIMATIONS; ODD NUMBER; PRODUCT;

D O I：

10.1063/1.4825615

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In a first stage the authors show how the exact distribution of the likelihood ratio statistic used to test the reality of a covariance matrix may be expressed as the distribution of the sum of two independent random variables, one with a Generalized Integer Gamma distribution and the other with the distribution of a sum of independent Logbeta random variables. From this form of the exact distribution the authors develop then a family of near-exact distributions, based on finite mixtures of Generalized Near-Integer Gamma distributions. These near-exact distributions match, by construction, some of the first exact moments and they have very manageable cumulative distribution functions, which allow for an easy computation of sharp near-exact quantiles and p-values.

引用

页码：797 / 800

页数：4