The purpose of this paper is to compare the sensitivity of the likelihood ratio test, Rao's score test, and the Wald test to the change of the nuisance parameters. The main result is that, with an error of magnitude O(n-1), the null distributions and the local alternative distributions of these tests are equally sensitive to nuisance parameter. We will also give accurate factorizations of these test statistics as quadratic forms, which are themselves useful for asymptotic analyses.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics