Large Deviations of Likelihood Ratio Statistics with Applications to Sequential Testing

摘要: We study the tail of null distribution $\log$ likelihood ratio statistic for testing sharp hypotheses about parameters an exponential family. show that classical chisquare approximation is exactly right order magnitude, although it may be off by a constant factor. then apply our results and techniques to find error probabilities sequential version test. The rejects if crosses given barrier time. Our approach uses local limit theorem which takes account large deviations integrates result using theory Hausdorff measures.