R. Grubel et Sm. Pitts, NONPARAMETRIC-ESTIMATION IN RENEWAL THEORY .1. THE EMPIRICAL RENEWAL FUNCTION, Annals of statistics, 21(3), 1993, pp. 1431-1451
We introduce a nonparametric estimator for the renewal function and di
scuss its properties, including consistency, asymptotic normality and
asymptotic validity of bootstrap confidence regions. The underlying th
eme is that stochastic models can be regarded as functionals or nonlin
ear operators. This view leads to nonparametric estimators in a natura
l way and statistical properties of the estimators can be related to t
he local behaviour of the functionals.