On Pinsker's Type Inequalities and Csiszar's f-divergences. Part I: Second and Fourth-Order Inequalities

Gustavo L. Gilardoni

We study conditions on $f$ under which an $f$-divergence $D_f$ will satisfy $D_f\ge c_f{V}^2$ or $D_f\ge c_{2,f}{V}^2+c_{4,f}{V}^4$, where $V$ denotes variational distance and t…