Asymptotic distributions of phi-divergences of hypothetical and observed frequencies on refined partitions

Abstract

For a wide class of goodness-of-fit statistics based on phi-divergences between hypothetical cell probabilities and observed relative frequencies, the asymptotic normality is established under the assumption n/m(n) --> gamma is an element of (0, infinity), where n denotes sample size and m(n) the number of cells. Related problems of asymptotic distributions of phi-divergence errors, and of phi-divergence deviations of histogram estimators from their expected values, are considered too.