Product-limit estimators of the gap time distribution of a renewal process under different sampling patterns

TL;DR

This paper discusses nonparametric methods for estimating the gap time distribution in renewal processes under various sampling schemes, highlighting the utility of simple product limit estimators despite their inefficiency.

Contribution

It introduces the application of simple product limit estimators to different sampling patterns in renewal processes, expanding their potential use in survival analysis.

Findings

Product limit estimators can be useful under various sampling schemes.

Despite inefficiency, simple estimators are practical in certain renewal process scenarios.

The paper clarifies the conditions where these estimators are applicable.

Abstract

Nonparametric estimation of the gap time distribution in a simple renewal process may be considered a problem in survival analysis under particular sampling frames corresponding to how the renewal process is observed. This note describes several such situations where simple product limit estimators, though inefficient, may still be useful.