Joint range of f-divergences

Many of the divergence measures used in statistics are of the f-divergence type. Often one is interested inequalities for one f-divergence in terms of another f-divergence. Such inequalities are for instance needed in order to calculate the relative efficiency of two f-divergences when used for testing goodness of fit but there are many other applications. In this paper we shall study the more general problem of determining the joint range of any pair of f-divergences. The results are useful in determining general conditions under which information divergence is a more efficient statistic for testing goodness of fit than another f-divergence, but will not be discussed in this short paper.