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Hoeffding Test and Divergence Tests Analysis


المفاهيم الأساسية
Divergence tests achieve first-order optimality but not second-order optimality compared to Neyman-Pearson test.
الملخص
  1. Introduction
    • Discusses binary hypothesis testing with divergence tests.
    • Analyzes second-order performance of Hoeffding test and divergence tests.
  2. Problem Setting
    • Defines divergence, composite hypothesis testing, and divergence tests.
  3. Divergence and Divergence Test
    • Defines divergence and divergence test.
    • Discusses invariant and non-invariant divergences.
  4. Examples of Divergences
    • Explains f-divergences and R´enyi divergence.
    • Introduces non-invariant divergences like Bregman divergences.
  5. Divergence Test
    • Describes the divergence test and its application.
  6. Second-Order Asymptotics of the Divergence Test
    • Presents the main results and theorem for second-order performance.
  7. Comparison with the Neyman-Pearson Test
    • Compares second-order terms of divergence test with Neyman-Pearson test.
  8. Numerical Results
    • Evaluates second-order performances of different hypothesis tests numerically.
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الإحصائيات
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.
اقتباسات
"The Hoeffding test is first-order optimal." "Divergence tests achieve the first-order term of the Neyman-Pearson test."

الرؤى الأساسية المستخلصة من

by K. V. Harsha... في arxiv.org 03-07-2024

https://arxiv.org/pdf/2403.03537.pdf
On the Second-Order Asymptotics of the Hoeffding Test and Other  Divergence Tests

استفسارات أعمق

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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