AFFINELY INVARIANT MATCHING METHODS WITH ELLIPSOIDAL DISTRIBUTIONS

• 成果类型: Article
• 署名作者: RUBIN, DB; THOMAS, N
• 署名单位: Educational Testing Service (ETS)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348671
• 发表日期: 1992
• 页码: 1079-1093
• 关键词: regression adjustment; DISCRIMINANT-ANALYSIS; remove bias; variables

摘要

Matched sampling is a common technique used for controlling bias in observational studies. We present a general theoretical framework for studying the performance of such matching methods. Specifically, results are obtained concerning the performance of affinely invariant matching methods with ellipsoidal distributions, which extend previous results on equal percent bias reducing methods. Additional extensions cover conditionally affinely invariant matching methods for covariates with conditionally ellipsoidal distributions. These results decompose the effects of matching into one subspace containing the best linear discriminant, and the subspace of variables uncorrelated with the discriminant. This characterization of the effects of matching provides a theoretical foundation for understanding the performance of specific methods such as matched sampling using estimated propensity scores. Calculations for such methods are given in subsequent articles.