Graduate Student Seminar

Speaker 1: Qing Ji

Title

Approximation of the Fisher Information Matrix in Poisson Mixture Mode

Abstract

Derivation of the Fisher Information Matrix (FIM) in the finite mixture model is tedious at least and usually not in closed form.  A diagonal matrix was proposed for a mixture of binomial distributions in (Blischke, 1962) as an approximation.  The performance of a similar type of approximation for a mixture of two Poisson distributions is evaluated and compared to the true FIM.  The result shows the performance varies under different parameters settings.  Difference between the true and approximated FIM is smaller as sample size and distance between means of two distributions increase.

Speaker 2: Gregory Haber

Title

Debiased Estimation in Group Testing With Inverse Binomial Sampling

Abstract

While group testing was first introduced in the statistical literature by Dorfman in 1943 as a means of classifying members of a given population, its use in the estimation of a binomial parameter has become an important area, with many interesting applications, since the 1960s. However, the primary tool for such estimation, the MLE, has several drawbacks, most notably a strong positive bias which has motivated much of the research in recent decades. In this talk we show, based on results of Degroot (1959), that an unbiased estimator in the group testing problem does exist under a specific inverse binomial sampling plan. Additionally, we introduce a debiased estimator under an alternative sampling plan for which no unbiased estimator exists which improves upon those in the current literature.