Smooth estimation of a monotone hazard and a monotone density under random censoring

Rik Lopuhaa, Eni Musta

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)

Abstract

We consider kernel smoothed Grenander-type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate n2/5 and that the limit distribution at a fixed point is Gaussian with explicitly given mean and variance. It is well known that standard kernel smoothing leads to inconsistency problems at the boundary points. It turns out that, also by using a boundary correction, we can only establish uniform consistency on intervals that stay away from the end point of the support (although we can go arbitrarily close to the right boundary).
Original languageEnglish
Pages (from-to)58-82
Number of pages25
JournalStatistica Neerlandica
Volume71
Issue number1
DOIs
Publication statusPublished - 20 Oct 2016

Keywords

  • isotonic estimation
  • hazard rate
  • smoothing
  • asymptotics
  • right censoring
  • Grenander estimator

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