Semiparametric Theory and Empirical Processes in Causal Inference

Kennedy, Edward H.

doi:10.1007/978-3-319-41259-7_8

Cited by 92 publications

(73 citation statements)

References 72 publications

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“…To show consistency under these conditions, we follow the approach of Tsiatis (2006) andKennedy (2016) by employing influence functions about the parameters. Define the estimating equation for λ as…”

Section: B3 Proof Of Propositionmentioning

confidence: 99%

A framework for covariate balance using Bregman distances

Josey

Juaréz-Colunga

Yang

et al. 2020

Scandinavian J Statistics

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A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear randomized. The propensity score is a natural quantity that arises in this setting. Propensity score weights have desirable asymptotic properties, but they often fail to adequately balance covariate data in finite samples. Empirical covariate balancing methods pose as an appealing alternative by exactly balancing the sample moments of the covariate distribution. With this objective in mind, we propose a framework for estimating balancing weights by solving a constrained convex program where the criterion function to be optimized is a Bregman distance. We then show that the different distances in this class render identical weights to those of other covariate balancing methods. A series of numerical studies are presented to demonstrate these similarities.

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Section: B3 Proof Of Propositionmentioning

confidence: 99%

A framework for covariate balance using Bregman distances

Josey

Juaréz-Colunga

Yang

et al. 2020

Scandinavian J Statistics

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show abstract

“…A crucial aspect of developing semiparametric theory and corresponding estimators for a given problem involves characterizing the possible influence functions, and in particular finding the efficient influence function. Many details on semiparametric theory are available elsewhere (Bickel et al ., ; van der Laan and Robins, ; Tsiatis, ; Kennedy, ), so we give only a brief review here. Any regular asymptotically linear estimator minus its target parameter can be expressed as the empirical average of its so‐called influence function plus an

o_{double-struckP} false(1 false/ \sqrt n false)

error term.…”

Section: Resultsmentioning

confidence: 99%

Robust Causal Inference with Continuous Instruments Using the Local Instrumental Variable Curve

Kennedy

Lorch

Small

2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Instrumental variables are commonly used to estimate effects of a treatment afflicted by unmeasured confounding, and in practice instruments are often continuous (e.g. measures of distance, or treatment preference). However, available methods for continuous instruments have important limitations: they either require restrictive parametric assumptions for identification, or else rely on modelling both the outcome and the treatment process well (and require modelling effect modification by all adjustment covariates). In this work we develop the first semiparametric doubly robust estimators of the local instrumental variable effect curve, i.e. the effect among those who would take treatment for instrument values above some threshold and not below. In addition to being robust to misspecification of either the instrument or treatment or outcome processes, our approach also incorporates information about the instrument mechanism and allows for flexible data‐adaptive estimation of effect modification. We discuss asymptotic properties under weak conditions and use the methods to study infant mortality effects of neonatal intensive care units with high versus low technical capacity, using travel time as an instrument.

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“…In this section we briefly review extensions and other uses of IFs. For deeper treatments of IFs and related topics, interested readers can see (Serfling, 1980;Pfanzagl, 1982;Bickel et al, 1993;van der Vaart, 2000;van der Laan and Robins, 2003;Tsiatis, 2006;Huber, 2011;Kennedy, 2016;Maronna et al, 2019).…”

Section: Discussionmentioning

confidence: 99%

Visually Communicating and Teaching Intuition for Influence Functions

Fisher

Kennedy

2020

The American Statistician

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Estimators based on influence functions (IFs) have been shown to be effective in many settings, especially when combined with machine learning techniques. By focusing on estimating a specific target of interest (e.g., the average effect of a treatment), rather than on estimating the full underlying data generating distribution, IF-based estimators are often able to achieve asymptotically optimal mean-squared error. Still, many researchers find IF-based estimators to be opaque or overly technical, which makes their use less prevalent and their benefits less available. To help foster understanding and trust in IF-based estimators, we present tangible, visual illustrations of when and how IF-based estimators can outperform standard "plug-in" estimators. The figures we show are based on connections between IFs, gradients, linear approximations, and Newton-Raphson.

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Semiparametric Theory and Empirical Processes in Causal Inference

Cited by 92 publications

References 72 publications

A framework for covariate balance using Bregman distances

A framework for covariate balance using Bregman distances

Robust Causal Inference with Continuous Instruments Using the Local Instrumental Variable Curve

Visually Communicating and Teaching Intuition for Influence Functions

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