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Hoeffding Test and Divergence Tests Analysis


Core Concepts
Divergence tests achieve first-order optimality but not second-order optimality compared to Neyman-Pearson test.
Abstract
Introduction Discusses binary hypothesis testing with divergence tests. Analyzes second-order performance of Hoeffding test and divergence tests. Problem Setting Defines divergence, composite hypothesis testing, and divergence tests. Divergence and Divergence Test Defines divergence and divergence test. Discusses invariant and non-invariant divergences. Examples of Divergences Explains f-divergences and R´enyi divergence. Introduces non-invariant divergences like Bregman divergences. Divergence Test Describes the divergence test and its application. Second-Order Asymptotics of the Divergence Test Presents the main results and theorem for second-order performance. Comparison with the Neyman-Pearson Test Compares second-order terms of divergence test with Neyman-Pearson test. Numerical Results Evaluates second-order performances of different hypothesis tests numerically.
Stats
2nDKL(PZn∥P) converges to a chi-square random variable with k-1 degrees of freedom. For α-divergences and KL divergence, (39) holds with δn = 1/√n.
Quotes
"The Hoeffding test is first-order optimal." "Divergence tests achieve the first-order term of the Neyman-Pearson test."

Deeper Inquiries

질문 1

다이버전스 테스트의 2차 성능을 어떻게 향상시킬 수 있을까요? Answer 1 here

질문 2

훼핑 테스트의 1차 최적성이 실무적으로 어떤 영향을 미치나요? Answer 2 here

질문 3

이 분석 결과가 통계학 분야에 미치는 영향은 무엇인가요? Answer 3 here
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