centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre


Keep in touch

Subscribe to cemmap news

Cross-fitting and fast remainder rates for semiparametric estimation

Authors: Whitney K. Newey and James M. Robins
Date: 03 October 2017
Type: cemmap Working Paper, CWP41/17
DOI: 10.1920/wp.cem.2017.4117


There are many interesting and widely used estimators of a functional with finite semi-parametric variance bound that depend on nonparametric estimators of nuisance func-tions. We use cross-fitting to construct such estimators with fast remainder rates. We give cross-fit doubly robust estimators that use separate subsamples to estimate different nuisance functions. We show that a cross-fit doubly robust spline regression estimator of the expected conditional covariance is semiparametric efficient under minimal conditions. Corresponding estimators of other average linear functionals of a conditional expectation are shown to have the fastest known remainder rates under certain smoothness conditions. The cross-fit plug-in estimator shares some of these properties but has a remainder term that is larger than the cross-fit doubly robust estimator. As specific examples we consider the expected conditional covariance, mean with randomly missing data, and a weighted average derivative.

Download full version

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us