The Numeraire E-Variable and Reverse Information Projection

A recent approach to statistical inference is based on the concept of an e-variable: a nonnegative sample statistic whose expected value is at most one if a given null hypothesis is true. This approach has been found to produce strong statistical error bounds and high statistical power and is easily extendible to sequential, or online, settings. E-variables admit a natural interpretation as the payoff of a financial bet. In this talk I will discuss how classical ideas from mathematical finance, in particular the numeraire portfolio, enables an optimality theory for e-variables that significantly generalizes earlier results. Our results also lead to a duality theory which yields the so-called reverse information projection in complete generality. Our work showcases the power of financial methods in a setting where information-theoretic tools have traditionally been preferred. (Joint work with Aaditya Ramdas and Johannes Ruf.)

About Martin Larsson

Martin Larsson is a professor in the Department of Mathematical Sciences at Carnegie Mellon University working in mathematical finance, probability theory, stochastic analysis, and statistics. Before joining CMU in 2019, he was an Assistant Professor of Mathematical Finance at the Department of Mathematics at ETH Zurich. He holds a PhD in Operations Research and Information Engineering from Cornell University, and was a postdoctoral fellow at the Swiss Finance Institute at EPFL in Lausanne. He is the mathematics representative on the Steering Committee of the Master of Science in Computational Finance (MSCF) program at CMU.