On the construction of unbiased estimators for the group testing problem

TL;DR

This paper explores the construction of unbiased estimators in group testing, extending beyond simple cases and demonstrating the impossibility of proper unbiased estimators in more complex scenarios with misclassification or multiple traits.

Contribution

It introduces constructions for unbiased estimators in broader group testing contexts and proves the non-existence of proper unbiased estimators outside standard cases.

Findings

Unbiased estimators can be constructed in certain group testing scenarios.

Proper unbiased estimators do not exist outside standard, misclassification-free cases.

The non-existence holds under various sampling plans, including binomial and multinomial.

Abstract

Debiased estimation has long been an area of research in the group testing literature. This has led to the development of several estimators with the goal of bias minimization and, recently, an unbiased estimator based on sequential binomial sampling. Previous research, however, has focused heavily on the simple case where no misclassification is assumed and only one trait is to be tested. In this paper, we consider the problem of unbiased estimation in these broader areas, giving constructions of such estimators for several cases. We show that, outside of the standard case addressed previously in the literature, it is impossible to find any proper unbiased estimator, that is, an estimator giving only values in the parameter space. This is shown to hold generally under any binomial or multinomial sampling plans