A Nonparametric Estimator of Heterogeneity Variance with Applications to SMR- and Proportion-Data
Dankmar Böhning, Jesus N. Sarol Jr. · Biometrical Journal · 2000
In this paper the situation of extra population heterogeneity is discussed from a analysis of variance point of view. We first provide a non-iterative way of estimating the variance of the heterogeneity distribution without estimating the heterogeneity distribution itself for Poisson and binomial counts. The consequences of the presence of heterogeneity in the estimation of the mean are discussed. We show that if the homogeneity assumption holds, the pooled mean is optimal while in the presence of strong heterogeneity, the simple (arithmetic) mean is an optimal estimator of the mean SMR or mean proportion. These results lead to the problem of finding an optimal estimator for situations not represented by these two extreme cases. We propose an iterative solution to this problem. Illustrations for the application of these findings are provided with examples from various areas.