The Effect of Bias, Variance Estimation, Skewness and Kurtosis of the Empirical Logit on Weighted Least Squares Analyses
研究了二项变量经验logit变换的偏误和前四阶累积量，发现现有偏误修正方法并非普遍有效，且经验logit分布比二项分布更偏斜、峰度更大，建议使用基于充分统计量的方法。
The bias and first four cumulants of the empirical logit transformation of a binomial variate are studied by means of asymptotic expansions and exact computation. The covariance of the empirical logit and its estimated variance is derived. Neither the +½ correction of Haldane (1955) and Anscombe (1956) nor the −½ suggested by Cox (1970) for weighted logit regression is universally effective in reducing bias. Other corrections are considered. The distribution of the empirical logit is shown to be considerably more skewed and to have a much larger kurtosis than the comparable binomial distribution. Methods based directly on sufficient statistics are preferred to those based on the empirical logit.