Affinely invariant matching methods with discriminant mixtures of proportional ellipsoidally symmetric distributions

Donald B. Rubin, Elizabeth Stuart

Research output: Contribution to journalArticle


In observational studies designed to estimate the effects of interventions or exposures, such as cigarette smoking, it is desirable to try to control background differences between the treated group (e.g., current smokers) and the control group (e.g., never smokers) on covariates X (e.g., age, education Matched sampling attempts to effect this control by selecting subsets of the treated and control groups with similar distributions of such covariates. This paper examines the consequences of matching using affinely invariant methods when the covariate distributions are "discriminant mixtures of proportional ellipsoidally symmetric" (DMPES) distributions, a class herein defined, which generalizes the ellipsoidal symmetry class of Rubin and Thomas [Ann. Statist. 20 (1992) 1079-1093]. The resulting generalized results help indicate why earlier results hold quite well even when the simple assumption of ellipsoidal symmetry is not met [e.g., Biometrics 52 (1996) 249-264]. Extensions to conditionally affinely invariant matching with conditionally DMPES distributions are also discussed.

Original languageEnglish (US)
Pages (from-to)1814-1826
Number of pages13
JournalAnnals of Statistics
Issue number4
Publication statusPublished - Aug 2006



  • Causal inference
  • Equal percent bias reducing (EPBR)
  • Matched sampling
  • Propensity scores

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

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