Near-exact distributions for the independence and sphericity likelihood ratio test statistics

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• 作者：Carlos A. Coelho ; Filipe J. Marques
• 关键词：Wilks lambda statistic ; Independence test ; Sphericity test ; Generalized Near-Integer Gamma distribution ; Mixtures
• 刊名：Journal of Multivariate Analysis
• 出版年：2010
• 出版时间：March 2010
• 年：2010
• 卷：101
• 期：3
• 页码：583-593
• 全文大小：681 K

文摘

In this paper we show how, based on a decomposition of the likelihood ratio test for sphericity into two independent tests and a suitably developed decomposition of the characteristic function of the logarithm of the likelihood ratio test statistic to test independence in a set of variates, we may obtain extremely well-fitting near-exact distributions for both test statistics. Since both test statistics have the distribution of the product of independent Beta random variables, it is possible to obtain near-exact distributions for both statistics in the form of Generalized Near-Integer Gamma distributions or mixtures of these distributions. For the independence test statistic, numerical studies and comparisons with asymptotic distributions proposed by other authors show the extremely high accuracy of the near-exact distributions developed as approximations to the exact distribution. Concerning the sphericity test statistic, comparisons with formerly developed near-exact distributions show the advantages of these new near-exact distributions.