Goodness-of-fit tests based on Rao''s divergence under sparseness assumptions

In many practical situations the classical (fixed-cells) assumptions to test goodness-of-fit are inappropriate, and we consider an alternative set of assumptions, which we call sparseness assumptions. It is proved that, under general conditions, the proposed family of statistics based on Rao's divergence is asymptotically normal when the sample size n and the number of cells M_n tend to infinity so that n/M_n→ν>0. This result is extended to contiguous alternatives, and subsequently it is possible to find the asymptotically most efficient member of the family.