The Probabilities of Large Deviations for the Chi-square and Log-likelihood Ratio Statistics

TL;DR

This paper derives new large deviation results for chi-square and log-likelihood ratio statistics, especially when the number of groups increases and group probabilities decrease as sample size grows.

Contribution

It introduces novel large deviation results for these statistics in the asymptotic regime of increasing groups and decreasing probabilities.

Findings

Large deviation bounds for chi-square and log-likelihood ratio statistics.

Results applicable when the number of groups grows and probabilities shrink.

Asymptotic behavior characterized for complex group structures.

Abstract

A new large deviation results for the Pearson chi-square and Log-likelihood ratio statistics are obtained. Here attention is focused on the case when the number of groups increases to infinity and the probabilities of groups decreases to zero, as the sample size tends to infinity.