{"doi":"10.3390/math9010089","title":"Changepoint in Error-Prone Relations","abstract":"<jats:p>Linear relations, containing measurement errors in input and output data, are considered. Parameters of these so-called errors-in-variables models can change at some unknown moment. The aim is to test whether such an unknown change has occurred or not. For instance, detecting a change in trend for a randomly spaced time series is a special case of the investigated framework. The designed changepoint tests are shown to be consistent and involve neither nuisance parameters nor tuning constants, which makes the testing procedures effortlessly applicable. A changepoint estimator is also introduced and its consistency is proved. A boundary issue is avoided, meaning that the changepoint can be detected when being close to the extremities of the observation regime. As a theoretical basis for the developed methods, a weak invariance principle for the smallest singular value of the data matrix is provided, assuming weakly dependent and non-stationary errors. The results are presented in a simulation study, which demonstrates computational efficiency of the techniques. The completely data-driven tests are illustrated through problems coming from calibration and insurance; however, the methodology can be applied to other areas such as clinical measurements, dietary assessment, computational psychometrics, or environmental toxicology as manifested in the paper.</jats:p>","journal":"Mathematics","year":2021,"id":641693,"datarank":0.24141568686511508,"base_score":1.6094379124341003,"endowment":1.6094379124341003,"self_citation_contribution":0.24141568686511508,"citation_network_contribution":0.0,"self_endowment_contribution":0.24141568686511508,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":4,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1668588,"name":"Michal Pešta","orcid":"0000-0001-5311-0797","position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Changepoint in Error-Prone Relations","abstract":"<jats:p>Linear relations, containing measurement errors in input and output data, are considered. 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