Distribution Estimates Consistent in χ2-Divergence

For a class of histogram based distribution estimators it is proved the consistency in chi(2)- divergence and expected chi(2)-divergence. For one of these estimators, introduced formerly by Barren, is also evaluated the rate of consistency in the expected chi(2)-divergence. These results are stronger than similar results formerly established in the literature for the total variation and Kullback's discrimination information, which are divergences dominated by the chi(2)-divergence.