Smooth and non-smooth estimates of a monotone hazard

TL;DR

This paper investigates monotone hazard estimation, addressing boundary inconsistency issues with penalization, and introduces methods for smoothing these estimates using kernel and penalization techniques.

Contribution

It proposes uniformly consistent hazard estimators with optimal penalization constants and discusses two smoothing methods based on non-smooth estimators.

Findings

Penalization yields boundary-consistent hazard estimates.

Optimal penalization constants are identified.

Two smoothing methods improve hazard estimate smoothness.

Abstract

We discuss a number of estimates of the hazard under the assumption that the hazard is monotone on an interval [0,a]. The usual isotonic least squares estimators of the hazard are inconsistent at the boundary points 0 and a. We use penalization to obtain uniformly consistent estimators. Moreover, we determine the optimal penalization constants, extending related work in this direction by Woodroofe and Sun (1993) and Woodroofe and Sun (1999). Two methods of obtaining smooth monotone estimates based on a non-smooth monotone estimator are discussed. One is based on kernel smoothing, the other on penalization.