{"title":"On Aggregation of Uncensored and Censored Observations","authors":"Sam Efromovich","doi":"10.3103/s1066530724700078","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In survival analysis a random right-censoring partitions data into uncensored and censored observations of the lifetime of interest. The dominance of uncensored observations is a familiar methodology in nonparametric estimation motivated by the classical Kaplan–Meier product-limit and Cox partial likelihood estimators. Nonetheless, for high rate censoring it is of interest to understand what, if anything, can be done by aggregating uncensored and censored observations for the staple nonparametric problems of density and regression estimation. The oracle, who knows distribution of the censoring lifetime, can use each subsample for consistent estimation and hence may shed light on the aggregation. The oracle’s asymptotic theory reveals that density estimation, based on censored observations, is an ill-posed problem with slower rates of risk convergence, the ill-posedness occurs in frequency-domain, its severity increases with frequency, and accordingly a special aggregation on low frequencies may be beneficial. On the other hand, censored observations are not ill-posed for nonparametric regression and the aggregation is feasible. Based on these theoretical results, methodology of aggregation in frequency domain is developed and proposed estimators are tested on simulated and real examples.</p>","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"36 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066530724700078","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
In survival analysis a random right-censoring partitions data into uncensored and censored observations of the lifetime of interest. The dominance of uncensored observations is a familiar methodology in nonparametric estimation motivated by the classical Kaplan–Meier product-limit and Cox partial likelihood estimators. Nonetheless, for high rate censoring it is of interest to understand what, if anything, can be done by aggregating uncensored and censored observations for the staple nonparametric problems of density and regression estimation. The oracle, who knows distribution of the censoring lifetime, can use each subsample for consistent estimation and hence may shed light on the aggregation. The oracle’s asymptotic theory reveals that density estimation, based on censored observations, is an ill-posed problem with slower rates of risk convergence, the ill-posedness occurs in frequency-domain, its severity increases with frequency, and accordingly a special aggregation on low frequencies may be beneficial. On the other hand, censored observations are not ill-posed for nonparametric regression and the aggregation is feasible. Based on these theoretical results, methodology of aggregation in frequency domain is developed and proposed estimators are tested on simulated and real examples.
期刊介绍：
Mathematical Methods of Statistics is an is an international peer reviewed journal dedicated to the mathematical foundations of statistical theory. It primarily publishes research papers with complete proofs and, occasionally, review papers on particular problems of statistics. Papers dealing with applications of statistics are also published if they contain new theoretical developments to the underlying statistical methods. The journal provides an outlet for research in advanced statistical methodology and for studies where such methodology is effectively used or which stimulate its further development.
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