Asymptotic laws for disparity statistics in product multinomial models

The paper presents asymptotic distributions of [phi]-disparity goodness-of-fit statistics in product multinomial models, under hypotheses and alternatives assuming sparse and nonsparse cell frequencies. The [phi]-disparity statistics include the power divergences of Read and Cressie (Goodness-of-fit Statistics for Discrete Multivariate Data, Springer, New York, 1988), the [phi]-divergences of Ciszár (Studia Sci. Math. Hungar. 2 (1967) 299) and the robust goodness of fit statistics of Lindsay (Ann. Statist. 22 (1994) 1081).