The Test of Full Specification of the Normal Distribution
نویسنده
چکیده
For a random sample X1, . . . , Xn from the normal distribution N (μ, σ) we test the hypothesis H : (μ, σ) = (0, 1) against K : (μ, σ) 6= (0, 1). Next to three classical tests – Likelihood ratio test, Wald test and Rao score test, we consider also special tests which were suggested for this problem in the literature. Within these tests we will be especially interested in the test which locally maximizes the average power, Isaacson’s approximation of the type D test and test based on Fisher’s combination of independent statistics. We investigate both local and global properties of these tests. The Monte Carlo study confirms the importance of the condition of local unbiasedness of the test. We also show the Bahadur efficiency to be a good concept of the global performance of the test in this problem.
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