Stein's Lemma - A Large Deviations Approach
NAVAL RESEARCH LAB WASHINGTON DC
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This report proves Steins Lemma by using a Large Deviations principle. The authors proof is general, direct, and intuitive. We represent the log-likelihood ratio used to test between the two hypotheses on the basis of the first n observations as a sample mean of i.i.d. observations. Led by the Strong Law of Large Numbers, we formulate a series of hypothesis tests that bound the true Neyman-Pearson tests. We then determine the asymptotic behavior of these tests by using arguments from the proof of Cramers Theorem. The conclusion of Steins Lemma follows.
- Statistics and Probability