Showing papers by "Hammou El Barmi published in 2012"
TL;DR: Improved estimators of the DFs are provided, it is shown that they are consistent, derive the weak convergence of the estimators, compare them with the empirical estimator, and provide formulas for statistical inferences.
6 citations
TL;DR: This article gives consistent estimators of all the CIFs and study the weak convergence of the resulting processes, which shows that the restricted estimators outperform the unrestricted ones in terms of mean square error.
Abstract: In the competing risks problem an important role is played by the cumulative incidence function (CIF), whose value at time t is the probability of failure by time t from a particular type of risk in the presence of other risks. Assume that the lifetime distributions of two populations are uniformly stochastically ordered. Since this ordering may not hold for the empiricals due to sampling variability, it is natural to estimate these distributions under this constraint. This will in turn affect the estimation of the CIFs. This article considers this estimation problem. We do not assume that the risk sets in the two populations are related, give consistent estimators of all the CIFs and study the weak convergence of the resulting processes. We also report the results of a simulation study that show that our restricted estimators outperform the unrestricted ones in terms of mean square error. A real life example is used to illustrate our theoretical results.