MMLD Inference of the Poisson and Geometric Models

This paper examines MMLD-based approximations for the inference of two univariate probability densities: the geometric distribution, parameterised in terms of a mean parameter, and the Poisson distribution. The focus is on both parameter estimation and hypothesis testing properties of the approximation. The new parameter estimators are compared to the MML87 estimators in terms of bias, squared error risk and KL divergence risk. Empirical experiments demonstrate that the MMLD parameter estimates are more biased, and feature higher squared error risk than the corresponding MML87 estimators. In contrast, the two criteria are virtually indistinguishable in the hypothesis testing experiment.