Resampling method in nonparametric estimation related to renewal processes

Let the statistical data be a collection of n piecesx ₁, ...,x _n of simple renewal processes. The random times between renewals have an unknown cumulative hazard function (c.h.f.) H₀(·). Let τ(H(·)) be the value of some functional τ(·), given c.h.f. H(·). The value τ₀=τ(H₀(·)) is a parameter of interest. If is an estimator for τ₀, then its quality can be characterized by the distribution law of normed deviations . These laws L_n are unknown, but they can be consistently estimated, by using the resampling method, as n→∞. In the case considered, the resampling method can be justified as a special case of the central limit resampling theorem. Supported by the Bank of Sweden Tercentenary Foundation. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.