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

Hendrik P. Lopuhaä and Eni Musta

Statistica Neerlandica, 2019, vol. 73, issue 2, 180-196

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.

Date: 2019
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