The Probabilities of Large Deviations for the Chi-square and   Log-likelihood Ratio Statistics
  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. 
Sherzod Mirakhmedov
math.ST math.PR stat.TH