We consider an estimate of the renewal function (rf) $H(t)$ using alimited number of independent observations of the interarrival timesfor an unknown interarrival-time distribution (itd). Thenonparametric estimate is derived from the rf-representation as series of distribution functions (dfs) ofconsecutive arrival times using a finite summation and approximations of the latter by empirical dfs.Due to the limited number of observed interarrival times theestimate is accurate just for closed time intervals $[0,t]$.An important aspect is given by the selection of an optimalnumber 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 itdsif the time interval is not too large, and (2) a data-dependentselection of $k$ by a bootstrap method.To evaluate boththe efficiency of the estimate and the selection methods of$k$, a Monte Carlo study is performed.
