One way to proceed would be to estimate the heterogeneity directly, and then constructed an adjusted estimator of the measures of interest by computing the heterogeneity distribution variance. Here, we will proceed differently. 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. Illustrations for the application of these findings are provided with examples from various areas such as disease mapping or meta-analysis. However, the way in which estimators are produced, is by no means unique.
Several estimators are possible.
Also, an estimator based on the quasi-likelihood approach is possible, though this needs to be constructed iteratively, and it will therefore be required to find reliable converging algorithms for it. The question arises, and this will be the objective of this project, which is experiences the best statistical properties. Statistics and Computing 3, 1-5. A note on a test for Poisson overdispersion. The distribution of the likelihood ratio for mixtures of densities from the one parameter exponential family.