The distance between a naive cumulative estimator and its least concave majorant

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

We consider the process Λ̂n−Λn, where Λn is a cadlag step estimator for the primitive Λ of a nonincreasing function λ on [0,1], and Λ̂n is the least concave majorant of Λn. We extend the results in Kulikov and Lopuhaä (2006, 2008) to the general setting considered in Durot (2007). Under this setting we prove that a suitably scaled version of Λ̂n−Λn converges in distribution to the corresponding process for two-sided Brownian motion with parabolic drift and we establish a central limit theorem for the Lp-distance between Λ̂n and Λn.

Original languageEnglish
Pages (from-to)119-128
Number of pages10
JournalStatistics and Probability Letters
Volume139
DOIs
Publication statusPublished - 2018

Keywords

  • Brownian motion with parabolic drift
  • Central limit theorem for L-distance
  • Grenander-type estimator
  • Least concave majorant
  • Limit distribution

Fingerprint Dive into the research topics of 'The distance between a naive cumulative estimator and its least concave majorant'. Together they form a unique fingerprint.

Cite this