A Proof of Orthogonal Double Machine Learning with $Z$-Estimators

Vasilis Syrgkanis

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arXiv · 1704.03754

A Proof of Orthogonal Double Machine Learning with $Z$-Estimators

Vasilis Syrgkanis

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Abstract

We consider two stage estimation with a non-parametric first stage and a generalized method of moments second stage, in a simpler setting than (Chernozhukov et al. 2016). We give an alternative proof of the theorem given in (Chernozhukov et al. 2016) that orthogonal second stage moments, sample splitting and $n^{1/4}$-consistency of the first stage, imply $\sqrt{n}$-consistency and asymptotic normality of second stage estimates. Our proof is for a variant of their estimator, which is based on the empirical version of the moment condition (Z-estimator), rather than a minimization of a norm of the empirical vector of moments (M-estimator). This note is meant primarily for expository purposes, rather than as a new technical contribution.

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stat.ML cs.LG math.ST stat.TH

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Vasilis Syrgkanis. 2017-04-12. A Proof of Orthogonal Double Machine Learning with $Z$-Estimators. https://arxiv.org/abs/1704.03754

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