Hoeffding Test and Divergence Tests Analysis

核心概念

Divergence tests achieve first-order optimality but not second-order optimality compared to Neyman-Pearson test.

要約

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.

統計

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.

引用

"The Hoeffding test is first-order optimal."
"Divergence tests achieve the first-order term of the Neyman-Pearson test."

抽出されたキーインサイト

On the Second-Order Asymptotics of the Hoeffding Test and Other Divergence Tests

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

https://arxiv.org/pdf/2403.03537.pdf

深掘り質問

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