Required Sample Size for Categorical Matching

This article investigates the sampling effort required to obtain matches for all members of a given sample. The exact distribution of the sample size required to complete the match quotas in all categories of the matching variable(s) is derived; the first two moments are also derived recursively, using a Markov chain approach. For problems with equal quotas in equiprobable categories, these moments may be computed as functions of gamma and normal order statistic moments. Numerical results are given to characterize the feasibility of matching in relation to the study size, the number of matching categories, and the distributions of the category probabilities and quotas.