Nonparametric estimation in renewal theory. II: Solutions of renewal-type equations

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.