The Probabilities of Large Deviations Associated with Multinomial Distributions

TL;DR

This paper investigates the probabilities of large deviations in multinomial distributions as the number of cells increases and cell-probabilities decrease, providing theoretical results for various statistics.

Contribution

It derives large deviation results for power-divergence and count statistics in complex multinomial settings, extending existing theoretical frameworks.

Findings

Large deviation probabilities are characterized for multinomial statistics.

Results apply to power-divergence and count-based statistics.

Theoretical bounds and asymptotic behaviors are established.

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.