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2015 Marginal integration for nonparametric causal inference
Jan Ernest, Peter Bühlmann
Electron. J. Statist. 9(2): 3155-3194 (2015). DOI: 10.1214/15-EJS1075

Abstract

We consider the problem of inferring the total causal effect of a single continuous variable intervention on a (response) variable of interest. We propose a certain marginal integration regression technique for a very general class of potentially nonlinear structural equation models (SEMs) with known structure, or at least known superset of adjustment variables: we call the procedure S-mint regression. We easily derive that it achieves the convergence rate as for nonparametric regression: for example, single variable intervention effects can be estimated with convergence rate $n^{-2/5}$ assuming smoothness with twice differentiable functions. Our result can also be seen as a major robustness property with respect to model misspecification which goes much beyond the notion of double robustness. Furthermore, when the structure of the SEM is not known, we can estimate (the equivalence class of) the directed acyclic graph corresponding to the SEM, and then proceed by using S-mint based on these estimates. We empirically compare the S-mint regression method with more classical approaches and argue that the former is indeed more robust, more reliable and substantially simpler.

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Jan Ernest. Peter Bühlmann. "Marginal integration for nonparametric causal inference." Electron. J. Statist. 9 (2) 3155 - 3194, 2015. https://doi.org/10.1214/15-EJS1075

Information

Received: 1 May 2014; Published: 2015
First available in Project Euclid: 25 January 2016

zbMATH: 1330.62171
MathSciNet: MR3453973
Digital Object Identifier: 10.1214/15-EJS1075

Subjects:
Primary: 62G05, 62H12

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.9 • No. 2 • 2015
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