Stein's Lemma - A Large Deviations Approach
Abstract
This report proves Stein's Lemma by using a Large Deviations principle. The author's 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 Cramer's Theorem. The conclusion of Stein's Lemma follows.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 21, 1989
- Accession Number
- ADA209090
Entities
People
- R. Sowers
Organizations
- United States Naval Research Laboratory