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Paper   IPM / M / 17637
School of Mathematics
  Title:   Estimation of a decreasing mean residual life based on ranked set sampling with an application to survival analysis
  Author(s):  Ehsan Zamanzade (Joint with Elham Zamanzade and A. Parvardeh)
  Status:   To Appear
  Journal: Int. J. Biostatistics
  Supported by:  IPM
The mean residual lifetime (MRL) of a unit in a population at a given time $t$, is the average remaining lifetime among those population units still alive at the time $t$. In some applications, it is reasonable to assume that MRL function is a decreasing function over time. Thus, one natural way to improve the estimation of MRL function is to use this assumption in estimation process. In this paper, we develop an MRL estimator in ranked set sampling (RSS) which, enjoys the monotonicity property. We prove that it is a strongly uniformly consistent estimator of true MRL function. We also show that the asymptotic distribution of the introduced estimator is the same as the empirical one, and therefore the novel estimator is obtained \lq\lq free of charge\rq \rq, at least in an asymptotic sense. We then compare the proposed estimator with its competitors in RSS and simple random sampling (SRS) using Monte Carlo simulation. Our simulation results confirm the superiority of the proposed procedure for finite sample sizes. Finally, a real dataset from the Surveillance, Epidemiology and End Results (SEER) program of the US National Cancer Institute (NCI) is used to show the application of the introduced technique for estimating the MRL function of patients with breast Cancer.

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