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arXiv 2402.147642024-02math.STecon.EMstat.TH

分层随机化的组合中心极限定理

A Combinatorial Central Limit Theorem for Stratified Randomization

Purevdorj Tuvaandorj

备注：: 29 pages, 1 figure

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AI总结：

本文提出在Lindeberg型条件下成立的分层随机化组合中心极限定理，可适配任意数量与大小的层（仅需每层至少两个单元），并将其用于推导多分层工具变量场景下两个检验统计量的渐近分布。

摘要：

本文建立了分层随机化的组合中心极限定理，该定理在Lindeberg型条件下成立。该定理允许任意数量或大小的层，唯一要求是每层至少包含两个单元。这种灵活性可同时适配数量不断增长的大层和小层，同时施加的条件极少。随后我们应用这一结果，推导了在存在可能众多、大小不受限制的层的情况下，为工具变量场景提出的两个检验统计量的渐近分布。

英文摘要：

This paper establishes a combinatorial central limit theorem for stratified randomization, which holds under a Lindeberg-type condition. The theorem allows for an arbitrary number or sizes of strata, with the sole requirement being that each stratum contains at least two units. This flexibility accommodates both a growing number of large and small strata simultaneously, while imposing minimal conditions. We then apply this result to derive the asymptotic distributions of two test statistics proposed for instrumental variables settings in the presence of potentially many strata of unrestricted sizes.

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