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.
Publié le : 1993-09-14
Classification:
Nonparametric estimation,
renewal functions,
functional central limit theorems,
bootstrap,
60K05,
62M09,
62G05
@article{1176349266,
author = {Grubel, Rudolf and Pitts, Susan M.},
title = {Nonparametric Estimation in Renewal Theory I: The Empirical Renewal Function},
journal = {Ann. Statist.},
volume = {21},
number = {1},
year = {1993},
pages = { 1431-1451},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349266}
}
Grubel, Rudolf; Pitts, Susan M. Nonparametric Estimation in Renewal Theory I: The Empirical Renewal Function. Ann. Statist., Tome 21 (1993) no. 1, pp. 1431-1451. http://gdmltest.u-ga.fr/item/1176349266/