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广义线性模型中三种经典检验的非零假设渐近分布AI 解读

This paper develops simple formulae for the asymptotic expansions up to order n−½ of the distributions of the likelihood ratio, Wald and score statistics in generalised linear models, under a sequence of Pitman alternatives. The powers of all three criteria, which are equivalent to first order, are compared under specific conditions based on second order approximations. The asymptotic distributions of all three statistics are obtained for testing a subset of linear…

广义线性模型的改进得分检验AI 解读

SUMMARY We present, in matrix notation, an asymptotic expansion for the null distribution of the score statistic in generalized linear models, corrected up to order n −1 where n is the sample size. The expansion has advantages for numerical purposes because it requires only simple operations on matrices. It is also sufficiently simple to be used analytically to obtain several closed form expressions, analogous to Bartlett corrections, in a variety of important score tests.…

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广义线性模型中的偏误校正AI 解读

SUMMARY In this paper we derive general formulae for first-order biases of maximum likelihood estimates of the linear parameters, linear predictors, the dispersion parameter and fitted values in generalized linear models. These formulae may be implemented in the GLIM program to compute bias-corrected maximum likelihood estimates to order n −1, where n is the sample size, with minimal effort by means of a supplementary weighted regression. For linear logistic models it is…

具有高阶卡方近似的修正得分检验统计量AI 解读

We give a general modified score test statistic whose nuil distribution is chi-squared to order n−1, where n is the sample size. The modified statistic depends on the joint cumulants of log likelihood derivatives for the full data. Some applications are discussed. Following Cox & Reid (1987a) we also derive a general formula for Bartlett-type corrections to improve test statistics whose null asymptotic distributions are chi-squared.

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指数族非线性模型的改进似然比统计量AI 解读

This paper gives a general formula for the expected likelihood ratio statistic for exponential family nonlinear models, corrected up to order n−1, where n is the sample size. This result generalizes previous work by Cordeiro (1983). Various general Bartlett adjustment formulae are given to some special models and improved likelihood ratio tests are discussed.

似然比统计量的修正AI 解读

Hayakawa's (1977) null asymptotic expansion of the likelihood ratio criterion for testing a composite null hypothesis against a composite alternative hypothesis appears to be in conflict with Lawley (1956) if and only if a certain coefficient is nonzero. It is shown that this coefficient vanishes for all regular problems. Correction factors are derived for generalized linear models when the scale factor is assumed unknown. The present paper generalizes also some results by…

似然比统计量的修正AI 解读

Hayakawa's (1977) null asymptotic expansion of the likelihood ratio criterion for testing a composite null hypothesis against a composite alternative hypothesis appears to be in conflict with Lawley (1956) if and only if a certain coefficient is nonzero. It is shown that this coefficient vanishes for all regular problems. Correction factors are derived for generalized linear models when the scale factor is assumed unknown. The present paper generalizes also some results by…

广义线性模型的改进似然比统计量AI 解读

Summary This paper gives a general formula for the expected value of the likelihood ratio statistic for generalized linear models, corrected up to terms of order n -1, where n is the size of the sample. The application of this formula to some models is illustrated.