Dr. Kolyan Ray

Asymptotic equivalence between two statistical models means that they
have the same asymptotic properties with respect to all decision
problems with bounded loss. A key result by Nussbaum states that
nonparametric density estimation is asymptotically equivalent to a
suitable Gaussian shift model, provided that the densities are smooth
enough and uniformly bounded away from zero.

We study the case when the latter assumption does not hold and the
density is possibly small. We further derive the optimal Le Cam distance
between these models, which quantifies how close they are. As an
application, we also consider Poisson intensity estimation with low
count data. This is joint work with Johannes Schmidt-Hieber.