Effects of Group Size on the MLE of Proportion in Group Testing

Under some conditions the proportion p of a certain trait can be estimated based on group testing. The method of group testing has several merits such as saving costs, protecting privacy etc. and has been applied to many fields. Its performance certainly depends on the selected group size. In particular, it was observed from practice that too large group size does not do a good job. There are lots of work on selecting the “optimal” group size. This article studies the effects of group size on the performance of the MLE of p by considering its bias and limiting distribution in the case of non-perfect group testing.