{"doi":"10.1093/jrsssb/qkad047","title":"Non-parametric inference about mean functionals of non-ignorable non-response data without identifying the joint distribution","abstract":"Abstract We consider identification and inference about mean functionals of observed covariates and an outcome variable subject to non-ignorable missingness. By leveraging a shadow variable, we establish a necessary and sufficient condition for identification of the mean functional even if the full data distribution is not identified. We further characterize a necessary condition for n-estimability of the mean functional. This condition naturally strengthens the identifying condition, and it requires the existence of a function as a solution to a representer equation that connects the shadow variable to the mean functional. Solutions to the representer equation may not be unique, which presents substantial challenges for non-parametric estimation, and standard theories for non-parametric sieve estimators are not applicable here. We construct a consistent estimator of the solution set and then adapt the theory of extremum estimators to find from the estimated set a consistent estimator of an appropriately chosen solution. The estimator is asymptotically normal, locally efficient and attains the semi-parametric efficiency bound under certain regularity conditions. We illustrate the proposed approach via simulations and a real data application on home pricing.","journal":"Journal of the Royal Statistical Society Series B (Statistical Methodology)","year":2023,"id":344329,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":13,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.944,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2023-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":280663,"name":"Wang Miao","orcid":"0000-0002-6221-2717","position":1,"is_corresponding":false},{"id":546382,"name":"Eric Tchetgen Tchetgen","orcid":null,"position":2,"is_corresponding":false},{"id":825498,"name":"Wei Li","orcid":"0000-0003-2461-2522","position":0,"is_corresponding":true}],"reference_count":54,"raw_metadata":null,"created_at":"2026-07-19T01:11:30.951510Z","pmid":"37521168","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":[]}