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关于似然比检验 Bartlett 调整的注记AI 解读

The invariance properties of the likelihood ratio statistic are used to question the validity of certain terms arising in the expansion of its null distribution. It is suggested that the null distribution of Bartlett adjusted tests is the appropriate reference chi-squared distribution with error of order n−3/2, where n is the sample size.

关于似然比检验 Bartlett 调整的一则说明AI 解读

The invariance properties of the likelihood ratio statistic are used to question the validity of certain terms arising in the expansion of its null distribution. It is suggested that the null distribution of Bartlett adjusted tests is the appropriate reference chi-squared distribution with error of order n−3/2, where n is the sample size.

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相关变量的方差齐性检验AI 解读

Four large-sample methods are proposed for testing the equality of the variances of a p-variate normal population. Two of the methods are asymptotically distribution robust against departures from the multinormality assumption of the parent population. In applying the tests no restrictive assumptions are made about the off-diagonal structure of the covariance matrics and no random splitting of the sample into subsamples is required. An example of the use of the tests is…

有效得分统计量零假设分布的渐近展开AI 解读

An asymptotic expansion for the null distribution of the efficient score statistic for testing a composite hypothesis in the presence of nuisance parameters is derived, and an interpretation of the terms occurring in the expansion is given. The use of the expansion to modify the percentage points of the large-sample reference x2 distribution is discussed. The first three moments of the null distribution are obtained and are used as a check on the accuracy of the algebra via…

相关变量的方差齐性检验AI 解读

Four large-sample methods are proposed for testing the equality of the variances of a p-variate normal population. Two of the methods are asymptotically distribution robust against departures from the multinormality assumption of the parent population. In applying the tests no restrictive assumptions are made about the off-diagonal structure of the covariance matrics and no random splitting of the sample into subsamples is required. An example of the use of the tests is…

有效得分检验统计量的局部功效AI 解读

The test statistic based on the efficient scores is shown to be locally biased in general. Comparisons of the local powers of this statistic, the likelihood ratio and maximum likelihood statistics reveal no uniform superiority properties. The performance of all three criteria in testing the sphericity hypothesis is examined and conditions which result in equivalence are discussed. A second example on testing for serial correlation suggests that computational simplicity may…

有效得分检验统计量的局部功效AI 解读

SUMMARY The test statistic based on the efficient scores is shown to be locally biased in general. Comparisons of the local powers of this statistic, the likelihood ratio and maximum likelihood statistics reveal no uniform superiority properties. The performance of all three criteria in testing the sphericity hypothesis is examined and conditions which result in equivalence are discussed. A second example on testing for serial correlation suggests that computational…