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

Journal article (2018)

Authors

H.P. Lopuhaä Statistics - EEMCS
E. Musta Statistics - EEMCS
Research Group
Statistics (EEMCS) (TU Delft)
Copyright: © 2018 H.P. Lopuhaä, E. Musta
DOI: https://doi.org/10.1111/stan.12153
More Info
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Published Date

2018

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

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.