Abstract
Let F denote the distribution function of a nonnegative population. Let H denote the corresponding renewal function. Given a random sample of size n from F, the sample renewal function Ĥ is defined as the renewal function of the sample distribution function. This is a nonlinear function of the sample distribution function. We give a proof of weak convergence of √ n ( Ĥ − H) in the Skorokhod topology. This strengthens a results of Frees [ Ann. Statist. 14 (1986), 1366-1378; Naval Res. Logist. 33 (1986), 361-372], who proved asymptotic normality of Ĥ( t) for each fixed t. Grubel and Pitts [ Ann. Statist. 21 (1993), 1431-1451] proved a more general result by a different method.
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