NONPARAMETRIC-ESTIMATION IN RENEWAL THEORY .1. THE EMPIRICAL RENEWAL FUNCTION

Authors
GRUBEL R PITTS SM
Citation
R. Grubel et Sm. Pitts, NONPARAMETRIC-ESTIMATION IN RENEWAL THEORY .1. THE EMPIRICAL RENEWAL FUNCTION, Annals of statistics, 21(3), 1993, pp. 1431-1451
Citations number
18
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annals of statistics → ACNP
ISSN journal
00905364
Volume
21
Issue
3
Year of publication
1993
Pages
1431 - 1451
Database
ISI
SICI code
0090-5364(1993)21:3<1431:NIRT.T>2.0.ZU;2-O
Abstract
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.