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Math Help - ratio test

  1. #1
    Super Member
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    ratio test

    what is the difference between neyman pearson lemma and likelihood ratio test?

    they seem like the same thing to me
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  2. #2
    Senior Member
    Joined
    Oct 2009
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    The Neyman-Pearson lemma is a result about constructing MP tests in the simple-null simple-alternative case, whereas LRT's are just forms of tests. Typically the NP-Lemma states that in the simple-null simple-alternative case, an appropriately chosen LRT is most powerful of a desired size (say alpha). However, particularly in the discrete case, a LRT of size alpha may or may not exist whereas the NP-Lemma, by utilizing randomized tests (which are NEVER LRT's), can always specify a most powerful size alpha test.

    One implication of the Neyman-Pearson lemma is that in the simple-null simple-alternative setup, a Likelihood Ratio Test is always most powerful of its size. The Neyman-Pearson lemma goes beyond this however, stating that a most powerful size alpha test always exists and states how to construct it, while a size alpha LRT doesn't necessarily exist.

    Outside of the simple-null simple-alternative setup, the NP-Lemma does not apply whereas it is always possible to construct a LRT.
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