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A central limit theorem for the Hellinger loss of Grenander-type estimators. / Lopuhaä, Hendrik P.; Musta, Eni.

In: Statistica Neerlandica, 2018, p. 1-17.

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@article{913df0a8c527490289320d5d772e36f7,
title = "A central limit theorem for the Hellinger loss of Grenander-type estimators",
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.",
keywords = "central limit theorem, Grenander estimator, Hellinger distance, isotonic estimation",
author = "Lopuha{\"a}, {Hendrik P.} and Eni Musta",
year = "2018",
doi = "10.1111/stan.12153",
language = "English",
pages = "1--17",
journal = "Statistica Neerlandica",
issn = "0039-0402",
publisher = "Blackwell",

}

RIS

TY - JOUR

T1 - A central limit theorem for the Hellinger loss of Grenander-type estimators

AU - Lopuhaä, Hendrik P.

AU - Musta, Eni

PY - 2018

Y1 - 2018

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85052644373&partnerID=8YFLogxK

U2 - 10.1111/stan.12153

DO - 10.1111/stan.12153

M3 - Article

AN - SCOPUS:85052644373

SP - 1

EP - 17

JO - Statistica Neerlandica

JF - Statistica Neerlandica

SN - 0039-0402

ER -

ID: 46747188