Discretization of (h, phi)-Divergences

Abstract In this paper, the problem of loss of information due to the discretization of continuous data and its estimate is studied. It is shown that the rate of convergence of the discretized versions of ( h , ϑ )-divergences to their continuous expressions is quadratic. The results of Ghurye and Johnson (1981) and Zografos, Ferentinos, and Papaioannou (1986) are generalized and supplemented for the ( h , ϑ )-divergence measures.