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Bias-reduced doubly robust estimation

Karel Vermeulen (UGent) and Stijn Vansteelandt (UGent)
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Abstract
Over the past decade, doubly robust estimators have been proposed for a variety of target parameters in causal inference and missing data models. These are asymptotically unbiased when at least one of two nuisance working models is correctly specified, regardless of which. While their asymptotic distribution is not affected by the choice of root-n consistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified, this choice of estimators can have a dramatic impact under misspecification of at least one working model. In this article, we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models, which is designed to improve the performance of the doubly robust estimator of interest, relative to the default use of maximum likelihood estimators for the nuisance parameters. The proposed approach locally minimizes the squared first-order asymptotic bias of the doubly robust estimator under misspecification of both working models and results in doubly robust estimators with easy-to-calculate asymptotic variance. It moreover improves the stability of the weights in those doubly robust estimators which invoke inverse probability weighting. Simulation studies confirm the desirable finite-sample performance of the proposed estimators. Supplementary materials for this article are available online.
Keywords
Double robustness, Missing data, Causal inference, Nuisance parameters, Semiparametric estimation, SEMIPARAMETRIC NONRESPONSE MODELS, DEMYSTIFYING DOUBLE ROBUSTNESS, MARGINAL STRUCTURAL MODELS, CAUSAL INFERENCE MODELS, INCOMPLETE DATA, ALTERNATIVE STRATEGIES, COVARIATE ADJUSTMENT, MISSING DATA, CONFOUNDERS, REGRESSION

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Citation

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Chicago
Vermeulen, Karel, and Stijn Vansteelandt. 2015. “Bias-reduced Doubly Robust Estimation.” Journal of the American Statistical Association 110 (511): 1024–1036.
APA
Vermeulen, Karel, & Vansteelandt, S. (2015). Bias-reduced doubly robust estimation. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 110(511), 1024–1036.
Vancouver
1.
Vermeulen K, Vansteelandt S. Bias-reduced doubly robust estimation. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION. 2015;110(511):1024–36.
MLA
Vermeulen, Karel, and Stijn Vansteelandt. “Bias-reduced Doubly Robust Estimation.” JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 110.511 (2015): 1024–1036. Print.
@article{5712066,
  abstract     = {Over the past decade, doubly robust estimators have been proposed for a variety of target parameters in causal inference and missing data models. These are asymptotically unbiased when at least one of two nuisance working models is correctly specified, regardless of which. While their asymptotic distribution is not affected by the choice of root-n consistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified, this choice of estimators can have a dramatic impact under misspecification of at least one working model. In this article, we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models, which is designed to improve the performance of the doubly robust estimator of interest, relative to the default use of maximum likelihood estimators for the nuisance parameters. The proposed approach locally minimizes the squared first-order asymptotic bias of the doubly robust estimator under misspecification of both working models and results in doubly robust estimators with easy-to-calculate asymptotic variance. It moreover improves the stability of the weights in those doubly robust estimators which invoke inverse probability weighting. Simulation studies confirm the desirable finite-sample performance of the proposed estimators. Supplementary materials for this article are available online.},
  author       = {Vermeulen, Karel and Vansteelandt, Stijn},
  issn         = {0162-1459},
  journal      = {JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION},
  language     = {eng},
  number       = {511},
  pages        = {1024--1036},
  title        = {Bias-reduced doubly robust estimation},
  url          = {http://dx.doi.org/10.1080/01621459.2014.958155},
  volume       = {110},
  year         = {2015},
}

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