Correction The probabilities of large deviations for a certain class of statistics associated with multinomial distributions

Abstract

We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel functions of cell-frequencies, are studied.Large deviation results for the power-divergence statistics and its most popular special variants, as well as for some count statistics are derived as consequences of general theorems.