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

Hendrik P. Lopuhaä; Eni Musta

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arXiv · 1612.06647

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

Hendrik P. Lopuhaä·Eni Musta

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Abstract

We consider Grenander type estimators for a monotone function $\lambda:[0,1]\to\mathbb{R}$, obtained as the slope of a concave (convex) estimate of the primitive of $\lambda$. Our main result is a central limit theorem for the Hellinger loss, which applies to statistical models that satisfy the setup in Durot (2007). This includes estimation of a monotone density, for which the limiting variance of the Hellinger loss turns out to be independent of $\lambda$.

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Hendrik P. Lopuhaä, Eni Musta. 2016-12-20. A central limit theorem for the Hellinger loss of Grenander type estimators. https://arxiv.org/abs/1612.06647

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