A central limit theorem for the Hellinger loss of Grenander‐type estimators. (12th August 2018) - Lopuhaä, Hendrik P.; Musta, Eni
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 .