Asymptotic Results for Truncated-censored and Associated Data

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.