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

Hendrik P. Lopuhaä; Eni Musta

doi:10.1111/stan.12153

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

Hendrik P. Lopuhaä, Eni Musta^*

^*Corresponding author for this work

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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 language	English
Pages (from-to)	180-196
Number of pages	17
Journal	Statistica Neerlandica
Volume	73 (2019)
Issue number	2
DOIs	https://doi.org/10.1111/stan.12153
Publication status	Published - 2018

Keywords

central limit theorem
Grenander estimator
Hellinger distance
isotonic estimation

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10.1111/stan.12153

stan.12153Final published version, 390 KBLicence: CC BY

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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.",

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AB - 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.

KW - central limit theorem

KW - Grenander estimator

KW - Hellinger distance

KW - isotonic estimation

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

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Keywords

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