All Dates/Times are Australian Eastern Standard Time (AEST)

Technical Program

Paper Detail

Paper IDD7-S2-T3.2
Paper Title Sub-Gaussian Error Bounds for Hypothesis Testing
Authors Yan Wang, Iowa State University, United States
Session D7-S2-T3: Hypothesis Testing
Chaired Session: Tuesday, 20 July, 22:20 - 22:40
Engagement Session: Tuesday, 20 July, 22:40 - 23:00
Abstract We interpret likelihood-based test functions from a geometric perspective where the Kullback-Leibler (KL) divergence is adopted to quantify the distance from a distribution to another. Such a test function can be seen as a sub-Gaussian random variable, and we propose a principled way to calculate its corresponding sub-Gaussian norm. Then an error bound for binary hypothesis testing can be obtained in terms of the sub-Gaussian norm and the KL divergence, which is more informative than Pinsker's bound when the significance level is prescribed. For $M$-ary hypothesis testing, we also derive an error bound which is complementary to Fano's inequality by being more informative when the number of hypotheses or the sample size is not large.