Estimating a ratio of means from bivariate counts with applications in stereology

Abstract

In survey sampling and in stereology, it is often desirable to estimate the ratio of means ?= E(Y)/E(X) from bivariate count data (X, Y) with unknown joint distribution. We review methods that are available for this problem, with particular reference to stereological applications. We also develop new methods based on explicit statistical models for the data, and associated model diagnostics. The methods are tested on a stereological dataset. For point-count data, binomial regression and bivariate binomial models are generally adequate. Intercept-count data are often overdispersed relative to Poisson regression models, but adequately fitted by negative binomial regression. © 2011 Australian Statistical Publishing Association Inc.