Comparison of Nonparametric Estimators for the Renewal Function

This paper addresses the problem of nonparametric estimation of the renewal function. Two estimators are discussed. The first estimator, introduced by Frees, is based on the sum of the convolutions without replacement of the empirical distribution function. We suggest a polynomial time algorithm to compute this estimator. The second estimator is based on the renewal function of the empirical distribution. We show how this estimator may be computed efficiently by solving a discretized renewal equation. In a simulation study the estimations are compared with respect to bias, mean-squared error and computing time