{"doi":"10.1214/24-aos2369","title":"Minimax rates for heterogeneous causal effect estimation","abstract":"Estimation of heterogeneous causal effects - i.e., how effects of policies and treatments vary across subjects - is a fundamental task in causal inference. Many methods for estimating conditional average treatment effects (CATEs) have been proposed in recent years, but questions surrounding optimality have remained largely unanswered. In particular, a minimax theory of optimality has yet to be developed, with the minimax rate of convergence and construction of rate-optimal estimators remaining open problems. In this paper we derive the minimax rate for CATE estimation, in a Hölder-smooth nonparametric model, and present a new local polynomial estimator, giving high-level conditions under which it is minimax optimal. Our minimax lower bound is derived via a localized version of the method of fuzzy hypotheses, combining lower bound constructions for nonparametric regression and functional estimation. Our proposed estimator can be viewed as a local polynomial R-Learner, based on a localized modification of higher-order influence function methods. The minimax rate we find exhibits several interesting features, including a non-standard elbow phenomenon and an unusual interpolation between nonparametric regression and functional estimation rates. The latter quantifies how the CATE, as an estimand, can be viewed as a regression/functional hybrid.","journal":"The Annals of Statistics","year":2024,"id":440299,"datarank":0.37273599746820013,"base_score":2.4849066497880004,"endowment":2.4849066497880004,"self_citation_contribution":0.37273599746820013,"citation_network_contribution":0.0,"self_endowment_contribution":0.37273599746820013,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":11,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.946,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2024-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1251888,"name":"Sivaraman Balakrishnan","orcid":"0000-0002-4538-8665","position":1,"is_corresponding":false},{"id":278790,"name":"James M. Robins","orcid":"0000-0001-6609-209X","position":2,"is_corresponding":false},{"id":1252290,"name":"L. H. Wasserman","orcid":null,"position":3,"is_corresponding":false},{"id":471278,"name":"Edward H. Kennedy","orcid":"0000-0002-0227-158X","position":0,"is_corresponding":true}],"reference_count":40,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-07-19T02:00:57.233748Z","pmid":"40171204","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}