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
Publication statusE-pub ahead of print - 2018

    Research areas

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

ID: 46747188