Bartlett Adjustments to the Likelihood Ratio Statistic and the Distribution of the Maximum Likelihood Estimator
本文针对一般参数模型，建立了对数似然比统计量的巴特利特调整因子与最大似然估计量条件分布中归一化常数之间的简单联系，从而证明用适当常数或估计因子除似然比统计量可改进其卡方近似。
SUMMARY For rather general parametric models, a simple connection is established between the Bartlett adjustment factor of the log-likelihood ratio statistic and the normalizing constant c of the formula c | ĵ |½ L̄ for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested. This leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi-squared approximation to its distribution. Various expressions for these quantities are discussed. In particular, for the case of a one-dimensional parameter an approximation to the constants involved is derived, which does not require integration over the sample space.