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Asymptotic Results for Truncated-censored and Associated Data

Zohra Guessoum () and Abdelkader Tatachak ()
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Zohra Guessoum: University of Science and Technology Houari Boumediene (USTHB)
Abdelkader Tatachak: University of Science and Technology Houari Boumediene (USTHB)

Sankhya B: The Indian Journal of Statistics, 2020, vol. 82, issue 1, No 6, 142-164

Abstract: Abstract 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: Associated data; Left truncation; Right censoring; Strong uniform consistency rate; Truncated-censored data; Primary 62G20; Secondary 62G05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13571-018-00185-4

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Handle: RePEc:spr:sankhb:v:82:y:2020:i:1:d:10.1007_s13571-018-00185-4