About the optimal estimation of a density with infinite support under Hellinger loss
Abstract
The aim of this paper is to give a complete description of the optimal estimation rates for the Hellinger loss when the square root of the density belongs to a Besov ball $\mathfrak{B}_{p,\infty}^{\alpha}(R)$. We make them explicit without further conditions when $p < 2$, and under a tail dominance condition when $p$ is larger. We also show that these rates can be improved when the density is assumed to be unimodal.
Domains
Statistics [math.ST]
Origin : Files produced by the author(s)