Comparison of Nonparametric Estimators for the Renewal Function

Helmut Schneider, Bin‐Shan Lin and Colm O'Cinneide

Journal of the Royal Statistical Society Series C, 1990, vol. 39, issue 1, 55-61

Abstract: 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 we show that the estimator based on the renewal equation has a slightly higher bias than the estimator introduced by Frees, while the mean‐squared errors are about the same. However, the computing time for the new estimator suggested in this paper is generally much smaller than that for Frees's estimator.

Date: 1990
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