{"doi":"10.1093/biomet/asaa019","title":"More efficient approximation of smoothing splines via space-filling basis selection","abstract":"We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size [Formula: see text], the smoothing spline estimator can be expressed as a linear combination of [Formula: see text] basis functions, requiring [Formula: see text] computational time when the number [Formula: see text] of predictors is two or more. Such a sizeable computational cost hinders the broad applicability of smoothing splines. In practice, the full-sample smoothing spline estimator can be approximated by an estimator based on [Formula: see text] randomly selected basis functions, resulting in a computational cost of [Formula: see text]. It is known that these two estimators converge at the same rate when [Formula: see text] is of order [Formula: see text], where [Formula: see text] depends on the true function and [Formula: see text] depends on the type of spline. Such a [Formula: see text] is called the essential number of basis functions. In this article, we develop a more efficient basis selection method. By selecting basis functions corresponding to approximately equally spaced observations, the proposed method chooses a set of basis functions with great diversity. The asymptotic analysis shows that the proposed smoothing spline estimator can decrease [Formula: see text] to around [Formula: see text] when [Formula: see text]. Applications to synthetic and real-world datasets show that the proposed method leads to a smaller prediction error than other basis selection methods.","journal":"Biometrika","year":2020,"id":95851,"datarank":0.5416376868966337,"base_score":3.6109179126442243,"endowment":3.6109179126442243,"self_citation_contribution":0.5416376868966337,"citation_network_contribution":0.0,"self_endowment_contribution":0.5416376868966337,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":36,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9495,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2020-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":245697,"name":"Xinlian Zhang","orcid":"0000-0002-0913-1205","position":1,"is_corresponding":false},{"id":475575,"name":"Jingyi Zhang","orcid":"0000-0002-7048-0930","position":2,"is_corresponding":false},{"id":331412,"name":"Wenxuan Zhong","orcid":"0000-0001-9006-622X","position":3,"is_corresponding":false},{"id":331413,"name":"Ping Ma","orcid":"0000-0002-5728-3596","position":4,"is_corresponding":false},{"id":331409,"name":"Cheng Meng","orcid":"0000-0002-7111-0966","position":0,"is_corresponding":true}],"reference_count":53,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-07-18T22:33:57.534608Z","pmid":"32831354","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":[]}