Limit Theory in Monotone Function Estimation

Cécile Durot, Hendrik P. Lopuhaä

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)


Abstract. We give an overview of the different concepts and methods that
are commonly used when studying the asymptotic properties of isotonic estimators.
After introducing the inverse process, we illustrate its use in establishing
weak convergence of the estimators at a fixed point and also weak
convergence of global distances, such as the Lp-distance and supremum distance.
Furthermore, we discuss the developments on smooth isotonic estimation.
Original languageEnglish
Pages (from-to)547-567
Number of pages21
JournalStatistical Science
Issue number4
Publication statusPublished - 2018


  • Cox model
  • current status model
  • isotonic estimation
  • limit theory
  • Lp-distance
  • maximum likelihood estimators
  • monotone density
  • monotone failure rate
  • monotone regression
  • supremum distance


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