The Annals of Statistics

Affinely Invariant Matching Methods with Ellipsoidal Distributions

Donald B. Rubin and Neal Thomas

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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.

Article information

Ann. Statist. Volume 20, Number 2 (1992), 1079-1093.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 62D05: Sampling theory, sample surveys
Secondary: 62H05: Characterization and structure theory 62A05 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 62K99: None of the above, but in this section

Matched sampling bias reduction Mahalanbois metric matching discriminant matching propensity score observational studies nonrandomized studies


Rubin, Donald B.; Thomas, Neal. Affinely Invariant Matching Methods with Ellipsoidal Distributions. Ann. Statist. 20 (1992), no. 2, 1079--1093. doi:10.1214/aos/1176348671.

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