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February 2000 Nonparametric estimation in renewal theory. II: Solutions of renewal-type equations
Susan M. Pitts, Konstadinos Politis
Ann. Statist. 28(1): 88-115 (February 2000). DOI: 10.1214/aos/1016120366

Abstract

Nonparametric estimators of solutions of renewal-type equations are proposed in terms of the empirical renewal function. Using the approach of Grübel and Pitts [Ann .Stat .21 1431 –1451 (1993)], who studied asymptotic properties of the empirical renewal function, a number of properties of our estimators are established, including strong consistency, asymptotic normality and efficiency, and asymptotic validity of bootstrap confidence bounds. The results are illustrated by some particular examples.

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Susan M. Pitts. Konstadinos Politis. "Nonparametric estimation in renewal theory. II: Solutions of renewal-type equations." Ann. Statist. 28 (1) 88 - 115, February 2000. https://doi.org/10.1214/aos/1016120366

Information

Published: February 2000
First available in Project Euclid: 14 March 2002

zbMATH: 1106.60311
MathSciNet: MR1762905
Digital Object Identifier: 10.1214/aos/1016120366

Subjects:
Primary: 60K05
Secondary: 62G05

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 1 • February 2000
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