A New Look at the Visual Performance of Nonparametric Hazard Rate Estimators

TL;DR

This paper adapts visual error criteria from density estimation to hazard rate estimation with censored data, providing insights into when these new criteria differ from traditional methods.

Contribution

It extends the visual error criteria to hazard rate estimation, offering a new perspective on evaluating nonparametric hazard estimators.

Findings

Derived results on the applicability of visual error criteria to hazard rate estimation

Identified conditions where visual criteria differ from conventional evaluation methods

Enhanced understanding of estimator performance in censored data contexts

Abstract

Nonparametric curve estimation by kernel methods has attracted widespread interest in theoretical and applied statistics. One area of conflict between theory and application relates to the evaluation of the performance of the estimators. Recently, Marron and Tsybakov (1995) proposed {\it visual error criteria} for addressing this issue of controversy in density estimation. Their core idea consists in using integrated alternatives to the Hausdorff distance for measuring the closeness of two sets based onthe Euclidean distance. In this paper, we transfer these ideas to hazard rate estimation from censored data. We are able to derive similar results that help to understand when the application of the new criteria will lead to answers that differ from those given by the conventional approaches.