Affinely invariant matching methods with ellipsoidal distributions
type: Item
instance of: scholarly article
title: Affinely invariant matching methods with ellipsoidal distributions
zbMATH Open document ID: 0761.62065
author: Donald B. Rubin
author: Neal Thomas
published in: The Annals of Statistics
publication date: 1992-09-27T00:00:00Z
review text: Consider the treated and control populations of size \(N_ t\) and \(N_ c\) respectively and \(X\) a set of matched variables recorded on all \(N_ t+N_ c\) units. Due to cost considerations, outcomes and additional covariates are recorded for matched subsamples of sizes \(n_ t\leq N_ t\) and \(n_ c\leq N_ c\) chosen such that the distributions of \(X\) among the \(n_ t\) and \(n_ c\) matched units are more similar than for random subsamples. The standard matched sample estimator of the treatment's effect on an outcome \(Y\) is \(\bar Y_ t-\bar Y_ c\) based on matched units. The bias of this estimator is less compared to the difference based on random subsamples. Consider ellipsoidal distributions for which there exists a linear transformation of the variables that results in a spherically symmetric distribution for the transformed variables. Matching methods based on population or sample inner products, such as discriminant matching or Mahalanobis metric matching or methods using propensity scores based on logistic regression estimators which are called affinely invariant, are used with ellipsoidal distributions. Furthermore, canonical forms for conditionally ellipsoidal distributions using conditionally affinely invariant matching methods are considered.
reviewed by: T. J. Rao
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62D05
zbMATH DE Number: 64519
zbMATH Keywords: bias reduction
zbMATH Keywords: observational studies
zbMATH Keywords: nonrandomized studies
zbMATH Keywords: matched subsamples
zbMATH Keywords: ellipsoidal distributions
zbMATH Keywords: spherically symmetric distribution
zbMATH Keywords: transformed variables
zbMATH Keywords: sample inner products
zbMATH Keywords: discriminant matching
zbMATH Keywords: Mahalanobis metric matching
zbMATH Keywords: propensity scores
zbMATH Keywords: logistic regression estimators
zbMATH Keywords: conditionally ellipsoidal distributions
zbMATH Keywords: conditionally affinely invariant matching methods
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348671
OpenAlex ID: W1972134466
DOI: 10.1214/AOS/1176348671
description: scientific article; zbMATH DE number 64519