Asymptotic power comparison of the chi-square and likelihood ratio tests

Summary A Hoeffding-type power comparison is made between the likelihood ratio and chi-square tests for a simple hypothesis in a multinomial. The power comparison is based on the fact that under an alternative hypothesis the distribution of the test statistic can be approximated by a normal distribution. The theory of large deviations is used to match the significance levels. This research was partially supported by the National Science Foundation Grant No. GP-33697X2, U.S. Energy Research and Development Agency Grant 7064100, Environmental Protection Agency Grant R805379-01-0 and U.S. Public Health Service Grant USPHS ES01299-15, at the University of California-Berkeley.