{"work":{"id":"2a799d79-cace-45bb-98a8-de5ca7ea05f3","openalex_id":null,"doi":null,"arxiv_id":"1801.09138","raw_key":null,"title":"Cross-Fitting and Fast Remainder Rates for Semiparametric Estimation","authors":null,"authors_text":"Cross-fitting and fast remainder rates for semiparametric estimation , author=","year":2018,"venue":"math.ST","abstract":"There are many interesting and widely used estimators of a functional with finite semiparametric variance bound that depend on nonparametric estimators of nuisance functions. We use cross-fitting (i.e. sample splitting) to construct novel estimators with fast remainder rates. We give cross-fit doubly robust estimators that use separate subsamples to estimate different nuisance functions. We obtain general, precise results for regression spline estimation of average linear functionals of conditional expectations with a finite semiparametric variance bound. We show that a cross-fit doubly robust spline regression estimator of the expected conditional covariance is semiparametric efficient under minimal conditions. Cross-fit doubly robust estimators of other average linear functionals of a conditional expectation are shown to have the fastest known remainder rates for the Haar basis or under certain smoothness conditions. Surprisingly, the cross-fit plug-in estimator also has nearly the fastest known remainder rate, but the remainder converges to zero slower 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.","external_url":"https://arxiv.org/abs/1801.09138","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-04T09:29:44.279362+00:00","pith_arxiv_id":"1801.09138","created_at":"2026-05-11T16:26:05.716913+00:00","updated_at":"2026-07-04T09:29:44.279362+00:00","title_quality_ok":true,"display_title":"Cross-Fitting and Fast Remainder Rates for Semiparametric Estimation","render_title":"Cross-Fitting and Fast Remainder Rates for Semiparametric Estimation"},"hub":{"state":{"work_id":"2a799d79-cace-45bb-98a8-de5ca7ea05f3","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":14,"external_cited_by_count":null,"distinct_field_count":7,"first_pith_cited_at":"2024-05-05T23:59:51+00:00","last_pith_cited_at":"2026-06-27T20:27:17+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-07-04T22:47:13.311359+00:00","tier_text":"hub"},"tier":"hub","role_counts":[],"polarity_counts":[],"runs":{},"summary":{},"graph":{},"authors":[]}}