{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/double-cross-fit-doubly-robust-estimators","title":"Double Cross-fit Doubly Robust Estimators: Beyond Series Regression","arxiv_id":"2403.15175","date":"2024-03-22","proceeding":null,"authors":["Alec McClean","Sivaraman Balakrishnan","Edward H. Kennedy","Larry Wasserman"],"abstract":"Doubly robust estimators with cross-fitting have gained popularity in causal inference due to their favorable structure-agnostic error guarantees. However, when additional structure, such as H\\\"{o}lder smoothness, is available then more accurate \"double cross-fit doubly robust\" (DCDR) estimators can be constructed by splitting the training data and undersmoothing nuisance function estimators on independent samples. We study a DCDR estimator of the Expected Conditional Covariance, a functional of interest in causal inference and conditional independence testing. We first provide a structure-agnostic error analysis for the DCDR estimator with no assumptions on the nuisance functions or their estimators. Then, assuming the nuisance functions are H\\\"{o}lder smooth, but without assuming knowledge of the true smoothness level or the covariate density, we establish that DCDR estimators with several linear smoothers are $\\sqrt{n}$-consistent and asymptotically normal under minimal conditions and achieve fast convergence rates in the non-$\\sqrt{n}$ regime. When the covariate density and smoothnesses are known, we propose a minimax rate-optimal DCDR estimator based on undersmoothed kernel regression. Moreover, we show an undersmoothed DCDR estimator satisfies a slower-than-$\\sqrt{n}$ central limit theorem, and that inference is possible even in the non-$\\sqrt{n}$ regime. Finally, we support our theoretical results with simulations, providing intuition for double cross-fitting and undersmoothing, demonstrating where our estimator achieves $\\sqrt{n}$-consistency while the usual \"single cross-fit\" estimator fails, and illustrating asymptotic normality for the undersmoothed DCDR estimator.","url_abs":"https://arxiv.org/abs/2403.15175v3","url_pdf":"https://arxiv.org/pdf/2403.15175v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"double-cross-fit-doubly-robust-estimators","repo_url":"https://github.com/alecmcclean/dcdr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"causal-inference","task_name":"Causal Inference"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"causal-inference","method_name":"Causal inference"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}