{"title":"THE ESTIMATION OF DISTRIBUTIONS UNDER A PARTICULAR RANDOM CENSORING","authors":"W. Lu","doi":"10.1515/9783112318867-049","DOIUrl":null,"url":null,"abstract":"Let X_1; X_2,…,X_N be i.i.d. random variables with distribution function F and censored by Y_1 Y_2…, Y_N. We can only observe (Z_t δ_t), i=1, 2,…, n and δ_i,i= n+1,…, N, where This model was proposed by Suzuki, K. (1985) and he discussed the case tnat X_t is a discrete random variable taking finite values. In this paper we discuss the case that X_t has a continuous distribution function F. We propose a estimator F of F and prove that N~(1/2)(F(t)-F(t)) converges to a Gussion process.","PeriodicalId":57248,"journal":{"name":"应用概率统计","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"1993-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/9783112318867-049","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"应用概率统计","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.1515/9783112318867-049","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let X_1; X_2,…,X_N be i.i.d. random variables with distribution function F and censored by Y_1 Y_2…, Y_N. We can only observe (Z_t δ_t), i=1, 2,…, n and δ_i,i= n+1,…, N, where This model was proposed by Suzuki, K. (1985) and he discussed the case tnat X_t is a discrete random variable taking finite values. In this paper we discuss the case that X_t has a continuous distribution function F. We propose a estimator F of F and prove that N~(1/2)(F(t)-F(t)) converges to a Gussion process.
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