Nonparametric Estimation in Renewal Theory I: The Empirical Renewal Function
The Annals of Statistics · 1993 · Volume 21 · Issue 3
Abstract
We introduce a nonparametric estimator for the renewal function and discuss its properties, including consistency, asymptotic normality and asymptotic validity of bootstrap confidence regions. The underlying theme is that stochastic models can be regarded as functionals or nonlinear operators. This view leads to nonparametric estimators in a natural way and statistical properties of the estimators can be related to the local behaviour of the functionals.
Keywords
60K05; 62G05; 62M09; bootstrap; functional central limit theorems; nonparametric estimation; renewal functions;
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