Efficient non-iterative and nonparametric estimation of heterogeneity variance for the standardized mortality ratio

In this paper the situation of extra population heterogeneity in the standardized mortality ratio is discussed from the point-of-view of an analysis of variance. First, some simple non-iterative ways are provided to estimate the variance of the heterogeneity distribution without estimating the heterogeneity distribution itself. Next, a wider class of linear unbiased estimators is introduced and their properties investigated. Consistency is shown for a wide sub-class of estimators charactererized by the fact that the associated linear weights are within some positive, finite bounds. Furthermore, it is shown that an efficient estimator is often provided when the weights are proportional to the expected counts.