Lower bounds on Information Divergence
  In this paper we establish lower bounds on information divergence from a distribution to certain important classes of distributions as Gaussian, exponential, Gamma, Poisson, geometric, and binomial. These lower bounds are tight and for several convergence theorems where a rate of convergence can be computed, this rate is determined by the lower bounds proved in this paper. General techniques for getting lower bounds in terms of moments are developed. 
Peter Harremo\"es and Christophe Vignat
cs.IT math.IT math.PR