Variational formulas for the power of the binary hypothesis testing problem with applications

To be considered for the 2016 IEEE Jack Keil Wolf ISIT Student Paper Award. Two variational formulas for the power of the binary hypothesis testing problem are derived. The first is given as the Legendre transform of a certain function and the second, induced from the first, is given in terms of the Cumulative Distribution Function (CDF) of the log-likelihood ratio. One application of the first formula is an upper bound on the power of the binary hypothesis testing problem in terms of the R´enyi divergence. The second formula provide a general framework for proving asymptotic and nonasymptotic expressions for the power of the test utilizing corresponding expressions for the CDF of the log-likelihood. The framework is demonstrated in the central limit regime (i.e., for non-vanishing type I error) and in the large deviations regime.

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: Nir Elkayam, Meir Feder
• Keywords: CORR 2016, Education