Comparison of LR, Score, and Wald Tests in a Non-IID Setting

Considering a large class of tests, we study higher order power in a possibly non-iid set-up. Optimum properties for the likelihood ratio and score tests are exhibited under the criteria of second-order local maximinity and third-order local average power, respectively. The issue of stringency with regard to third-order average power has been addressed. We also compare the power properties of various Bartlett-type adjustments for the tests.