Exponential Concentration of a Density Functional Estimator

03/28/2016
by   Shashank Singh, et al.
0

We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For densities on the d-dimensional unit cube [0,1]^d that lie in a β-Hölder smoothness class, we prove our estimator converges at the rate O ( n^-β/β + d). Furthermore, we prove the estimator is exponentially concentrated about its mean, whereas most previous related results have proven only expected error bounds on estimators.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset