Abstract
This paper focuses on the likelihood ratio test (LRT) statistics for different hypothesis tests. Assuming that a random sample is from a normal population, we make the sample size n and the dimension p close to infinity and satisfy p < n − c for some 1 ≤ c ≤ 4 . Based on this assumption, the moderate deviation principle (MDP) for the LRT will be given under the null hypothesis. The corresponding numerical simulation results are shown at the end of the paper.
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