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存在干扰参数时置信限的渐近展开及应用AI 解读

SUMMARY Series expansions for confidence limits based on consistent estimators are obtained in the presence of nuisance parameters. The maximum likelihood estimator is treated as a special case and the necessary characteristics of its sampling distribution are obtained in terms of basic quantities derivable from the likelihood function. The theory is applied to the problem of setting separate confidence limits for the scale and shape parameters of the Weibull distribution.…

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…

贝叶斯点估计量的抽样性质AI 解读

The sampling distributions of various Bayesian point estimators are examined and it is shown that by choosing an appropriate prior distribution for the unknown parameter such estimators can be less biased than the maximum likelihood estimator. It is also shown that a pivotal quantity can be developed by a suitable transformation of the unknown parameter.

贝叶斯点估计量的抽样性质AI 解读

The sampling distributions of various Bayesian point estimators are examined and it is shown that by choosing an appropriate prior distribution for the unknown parameter such estimators can be less biased than the maximum likelihood estimator. It is also shown that a pivotal quantity can be developed by a suitable transformation of the unknown parameter.

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似然比及相关检验准则AI 解读

A more accurate approximation is derived for the power function of the likelihood ratio criterion for testing a simple null hypothesis against a class of composite alternative hypotheses. Two rival test statistics suggested by Rao (1965) and asymptotically equivalent to the likelihood ratio procedure are examined and approximations are obtained to their distributions under the null and alternative hypotheses. Comparisons between the power functions of all three statistics…

基于加权似然积分的置信点公式AI 解读

SUMMARY Lindley’s problem, relating to the conditions under which there is formal mathematical equivalence between Bayesian solutions and confidence theory solutions, is discussed. A result concerning location parameters is extended. The corresponding asymptotic theory is developed and a modification of the problem is also discussed.