Difficulties in Obtaining Consistent Estimators of Variance Parameters
研究了当均值是未知干扰参数时，如何从大量小样本中估计方差。发现当方差与均值平方成比例时，边际似然可得到一致估计，但该方法无法推广到其他方差函数，并探讨了其他似然方法。
This paper considers the estimation of variances by pooling information from a large number of small samples, when the means are nuisance parameters about which no assumptions or prior knowledge are available. When the variance is proportional to the square of the mean we obtain a consistent estimator from a marginal likelihood. However, this method cannot be generalized to other variance functions. Integrated likelihood, modified likelihood and partial conditional likelihood methods are investigated for this example and suggest methods for the general case when the standard deviation is small compared with the mean.