Cross-fitting and fast remainder rates for semiparametric estimation

By Whitney K. Newey, Jamie Robins. 2017

175 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

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Citations in the corpus

The hardness of conditional independence testing and the generalised covariance measure (2018, background): “Though typically not thought of as conditional independence tests, there are several approaches to estimating the expected conditional covariance functional Ecov(X,Y |Z) in the semiparametric statistics literature [42, 15, 36].”
Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, background): “Intuitively, this condition arises from a “leave-in” type remainder, and as such, it can be weakened using cross splitting Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, Newey, and Robins (2018); Newey and Robins (2018). We opt to maintain (c) exactly because deep nets are not amenable to either”
Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, methodology): “Newey and Robins (2018) present and analyze estimators based on regression splines, while we present and analyze sparse estimators methods for the high-dimensional setting.”
The Balancing Act in Causal Inference (2021, background): “In particular, Newey and Robins (2018) show that with specialized estimators of both γipw and m1 that are amenable to careful analysis of the orthogonality of δγ and δm, the AIPW estimator has nearly the same asymptotic behavior.16 Work like this, which brings us closer to understanding what is…”
Augmented minimax linear estimation (2017, background): “Furthermore, for some specific choices of estimators γ̂ψ(·) and m̂(·), it has been shown that the errors in estimating the nuisance parameters are sufficiently orthogonal that the rate-product bound can be relaxed (Newey and Robins, 2018).”
A Calibration Metric for Risk Scores with Survival Data (2019, background): “For a general discussion of this approach, see Chernozhukov et al. (2018) and Newey and Robins (2018).”
Leave‐Out Estimation of Variance Components (2018, unknown): “While the first interval employs a normal approximation, the latter two allow for weak identification by employing non-standard limiting distributions involving linear combinations of normal and χ2 random variables.”
Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score. (2018, background): “Newey & Robins (2018) showed that the sample splitting technique can improve the convergence rate of the remainder terms for semiparametric models.”
Locally Robust Semiparametric Estimation (2016, background): “Fourth, in important settings debiased GMM has faster remainder rates than plug-in GMM, e.g. Newey and Robins (2017).”