Consistent estimation of the structural distribution function

Motivated by problems in linguistics we consider a multinomial random vecto r for which the number of cells N is not much smaller than the sum of the c ell frequencies, i.e. the sample size n. The distribution function of the u niform distribution on the set of all cell probabilities multiplied by N Is railed the structural distribution function of the cell probabilities. Con ditions are given that guarantee that the structural distribution function can be estimated consistently as n increases indefinitely although n/N does not. The natural estimator Is inconsistent and we prove consistency of ess entially two alternative estimators.