Required Sample Size for Categorical Matching
研究了为给定样本中所有成员找到匹配所需的样本量，推导了完成匹配配额的样本量的精确分布和前两阶矩，并给出了数值结果以评估匹配的可行性。
Abstract 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.