A Note on Wald's Type Chi-squared Tests of Fit

被引：2

作者：

Voinov, Vassilly ^{[1
,2
]}

机构：

[1] KIMEP Univ, Alma Ata, Kazakhstan

[2] Minist Educ & Sci Republ Kazakhstan, Kazakhstan Inst Math & Math Modeling, Alma Ata, Kazakhstan

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2015年 / 44卷 / 21期

关键词：

Khatri's lemma; Matrix generalized inverse; Maximum likelihood estimator (MLE); Method of moments estimator (MME); Modified chi-squared tests; Standardized frequencies; Wald's method;

D O I：

10.1080/03610926.2013.768668

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The Wald's method for constructing chi-squared tests of fit has been formulated more accurately. It is shown that Wald's type statistics will follow the central chi-squared distribution if and only if the limit covariance matrix of standardized frequencies will not depend on unknown parameters. Several examples that illustrate this important fact are presented. In particular, it is shown that the goodness-of-fit statistic developed by Moore and Stubblebine does not follow the chi-squared limit distribution, and, hence, cannot be used for testing multivariate normality.

引用

页码：4622 / 4630

页数：9

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