ASYMPTOTICS OF THE SAMPLE RENEWAL FUNCTION

Let F denote the distribution function of a nonnegative population. Le t H denote the corresponding renewal function. Given a random sample o f size n from F, the sample renewal function ($) over cap H is defined as the renewal function of the sample distribution function. This is a nonlinear function of the sample distribution function. We give a pr oof of weak convergence of root n (($) over cap H - H) in the Skorokho d topology. This strengthens a results of Frees [Ann. Statist. 14 (198 6), 1366-1378; Naval Res. Logist. 33 (1986), 361-372], who proved asym ptotic normality of ($) over cap H(t) for each fixed t. Grubel and Pit ts [Ann. Statist. 21 (1993), 1431-1451] proved a more general result b y a different method. (C) 1995 Academic Press, Inc.