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

Journal Article (2018)
Author(s)

Hendrik P. Lopuhaä (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Eni Musta (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Research Group
Statistics
DOI related publication
https://doi.org/10.1111/stan.12153 Final published version
More Info
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Publication Year
2018
Language
English
Research Group
Statistics
Issue number
2
Volume number
73 (2019)
Pages (from-to)
180-196
Downloads counter
148
Collections
Institutional Repository
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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.