A central limit theorem for the Hellinger loss of Grenander‐type estimators. (12th August 2018)

• Record Type: Journal Article
• Authors: Lopuhaä, Hendrik P.; Musta, Eni
• Is Part Of: Statistica Neerlandica. Volume 73:Number 2(2019)
• Page Start: 180
• Page End: 196
• Publication Date: 2018-08-12
• Subjects: central limit theorem -- Grenander estimator -- Hellinger distance -- isotonic estimation; Statistics -- Periodicals; 519.5; 314.92
• DOI: 10.1111/stan.12153
• Languages: English
• ISSNs: 0039-0402

Abstract

Abstract : We consider Grenander‐type estimators for a monotone function λ : [ 0, 1 ] → R +, 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 .