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

Abstract

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.

Some results from an earlier version of this preprint have been moved to arXiv:1802.03425

Cited by in corpus (4)

• Local asymptotic equivalence of pure quantum states ensembles and quantum Gaussian white noise
• Adaptive minimax optimality in statistical inverse problems via SOLIT -- Sharp Optimal Lepskii-Inspired Tuning
• Optimal regularized hypothesis testing in statistical inverse problems
• Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities