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."