A Lower Bound on Arbitrary $f$--Divergences in Terms of the Total Variation

Abstract: An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among the f-divergences. It is shown that every f-divergence is bounded from below by a monotonous function of the total variation. Under appropriate regularity conditions, this function is shown to be monotonous. Remark: The proof of the main proposition is relatively easy, whence it is highly likely that the result is known. The author would be very grateful for any information regarding references or related work.