A central limit theorem for the Hellinger loss of Grenander-type estimators

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Abstract

We consider Grenander-type estimators for a monotone function (Formula presented.), obtained as the slope of a concave (convex) estimate of the primitive of λ. Our main result is a central limit theorem for the Hellinger loss, which applies to estimation of a probability density, a regression function or a failure rate. In the case of density estimation, the limiting variance of the Hellinger loss turns out to be independent of λ.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalStatistica Neerlandica
DOIs
Publication statusE-pub ahead of print - 2018

Keywords

  • central limit theorem
  • Grenander estimator
  • Hellinger distance
  • isotonic estimation

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