Markovitch, Natalia M.Natalia M.MarkovitchKrieger, Udo R.Udo R.Krieger2019-09-192014-09-2420061532-6349https://fis.uni-bamberg.de/handle/uniba/14867We consider an estimate of the renewal function (rf) H(t) using a limited number of independent observations of the interarrival times for an unknown interarrival-time distribution (itd). The nonparametric estimate is derived from the rf-representation as a series of distribution functions (dfs) of consecutive arrival times using a finite summation and approximations of the latter by empirical dfs. Due to the limited number of observed interarrival times, the estimate is accurate just for closed time intervals [0, t]. An important aspect is given by the selection of an optimal number of terms k of the finite sum. Here two methods are proposed: (1) an a priori choice of k as function of the sample size l which provides almost surely (a.s.) the uniform convergence of the estimate to the rf for light- and heavy-tailed itds if the time interval is not too large, and (2) a data-dependent selection of k by a bootstrap method. To evaluate both the efficiency of the estimate and the selection methods of k, a Monte Carlo study is performed.engBootstrap methodNonparametric estimateRenewal functionarticle10.1080/15326340600648922