arXiv subjects

Eni Musta

Publications and source records attributed to Eni Musta.

20 records · Page 2Linked to original sources

arXiv2016

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

We consider Grenander type estimators for a monotone function $λ:[0,1]\to\mathbb{R}$, 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 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 $λ$.

math.ST↗

arXiv2015

Functional Cramer-Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes

We investigate the problems of drift estimation for a shifted Brownian motion and intensity estimation for a Cox process on a finite interval $[0,T]$, when the risk is given by the energy functional associated to some fractional Sobolev space $H^1_0\subset W^{α,2}\subset L^2$. In both situations, Cramer-Rao lower bounds are obtained, entailing in particular that no unbiased estimators with finite risk in $H^1_0$ exist. By Malliavin calculus techniques, we also study super-efficient Stein type estimators (in the Gaussian case).

math.ST↗