Cross-fitting and fast remainder rates for semiparametric estimation
Whitney K. Newey () and
James M. Robins
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Whitney K. Newey: Institute for Fiscal Studies and MIT
James M. Robins: Institute for Fiscal Studies
No CWP41/17, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies
There are many interesting and widely used estimators of a functional with ?nite semi-parametric variance bound that depend on nonparametric estimators of nuisance func-tions. We use cross-?tting to construct such estimators with fast remainder rates. We give cross-?t doubly robust estimators that use separate subsamples to estimate di?erent nuisance functions. We show that a cross-?t doubly robust spline regression estimator of the expected conditional covariance is semiparametric e?cient 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-?t plug-in estimator shares some of these properties but has a remainder term that is larger than the cross-?t doubly robust estimator. As speci?c examples we consider the expected conditional covariance, mean with randomly missing data, and a weighted average derivative.
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