The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Mathematical Statistics and Learning


Full-Text PDF (486 KB) | Metadata | Table of Contents | MSL summary
Online access to the full text of Mathematical Statistics and Learning is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
Volume 1, Issue 2, 2018, pp. 101–170
DOI: 10.4171/MSL/1-2-1

Published online: 2018-09-05

The Le Cam distance between density estimation, Poisson processes and Gaussian white noise

Kolyan Ray[1] and Johannes Schmidt-Hieber[2]

(1) Leiden University, Netherlands
(2) Leiden University, Netherlands

It is well known that density estimation on the unit interval is asymptotically equivalent to a Gaussian white noise experiment, provided the densities have Hölder smoothness larger than 1/2 and are uniformly bounded away from zero. We derive matching lower and constructive upper bounds for the Le Cam deficiencies between these experiments, with explicit dependence on both the sample size and the size of the densities in the parameter space. As a consequence, we derive sharp conditions on how small the densities can be for asymptotic equivalence to hold. The related case of Poisson intensity estimation is also treated.

Keywords: Asymptotic equivalence, Le Cam distance, density estimation, Poisson intensity estimation, Gaussian shift experiments

Ray Kolyan, Schmidt-Hieber Johannes: The Le Cam distance between density estimation, Poisson processes and Gaussian white noise. Math. Stat. Learn. 1 (2018), 101-170. doi: 10.4171/MSL/1-2-1