The Annals of Statistics

Nonparametric Estimation in Renewal Theory I: The Empirical Renewal Function

Rudolf Grubel and Susan M. Pitts

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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.

Article information

Source
Ann. Statist., Volume 21, Number 3 (1993), 1431-1451.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349266

Digital Object Identifier
doi:10.1214/aos/1176349266

Mathematical Reviews number (MathSciNet)
MR1241273

Zentralblatt MATH identifier
0818.62037

JSTOR
links.jstor.org

Subjects
Primary: 60K05: Renewal theory
Secondary: 62M09: Non-Markovian processes: estimation 62G05: Estimation

Keywords
Nonparametric estimation renewal functions functional central limit theorems bootstrap

Citation

Grubel, Rudolf; Pitts, Susan M. Nonparametric Estimation in Renewal Theory I: The Empirical Renewal Function. Ann. Statist. 21 (1993), no. 3, 1431--1451. doi:10.1214/aos/1176349266. https://projecteuclid.org/euclid.aos/1176349266


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See also

  • Part II: Konstadinos Politis, Susan M. Pitts. Nonparametric Estimation in Renewal Theory. II. Solutions of Renewal-type Equations. Ann. Statist., vol. 28, no. 1 (2000), 88-115.