Asymptotic Results for Truncated-censored and Associated Data
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Left-truncation and right-censoring arise frequently when considering lifetime data. When both incompleteness conditions occur, a product-limit estimator was proposed and investigated in the independent case by Tsai et al. (Biometrika74, 883–886, 1987). In the presence of covariates, the conditional version was studied in the α-mixing setting by Liang et al. (Test21, 790–810, 2012). Our objective in the present paper is to derive strong uniform consistency rates for the cumulative hazard and the product-limit estimates when the lifetime observations form an associated sequence. Then, as an application we derive a strong uniform consistency rate for the kernel estimator of the hazard rate function considered by Uzunoḡullari and Wang (Biometrika79, 297–310, 1992) in the iid case.
Keywords and phrasesAssociated data Left truncation Right censoring Strong uniform consistency rate Truncated-censored data
AMS (2000) subject classificationPrimary 62G20 Secondary 62G05
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The authors are indebted to an anonymous referee and the Editor, whose constructive comments and suggestions helped to improve an earlier version of this paper. Many thanks also to Professor Mohamed Lemdani at the Faculty of Pharmaceutical Sciences and Biology (University Lille 2) for many valuable comments on this work.
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