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Comparison of Nonparametric Estimators for the Renewal Function
Author(s) -
Schneider Helmut,
Lin BinShan,
O'Cinneide Colm
Publication year - 1990
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347811
Subject(s) - nonparametric statistics , estimator , statistics , mathematics , econometrics , function (biology) , biology , evolutionary biology
SUMMARY 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.