Log-optimal anytime-valid E-values

International Journal of Approximate Reasoning, vol. 141, pp. 69–82

Abstract

We consider the problem of measuring statistical evidence against a composite null hypothesis. We base our approach on the concept of an E-value, which measures evidence by the multiplication factor achieved by engaging in bets that are fair under the null. We adopt the log-optimality criterion for choosing among all possible E-values, which was considered earlier for a fixed sample size. We extend these ideas to sequential testing under optional stopping, by revisiting anytime-valid E-values. Our main contribution is the formulation of a sequential log-optimality criterion. We study its properties, and work out examples analytically and computationally.

Authors 2

1. Wouter M. Koolen corresponding

   Centrum Wiskunde & Informatica

   Affiliation as printed

   Centrum Wiskunde & Informatica, Netherlands

2. Peter Grünwald Aachen

   Leiden University · Centrum Wiskunde & Informatica

   Affiliation as printed

   Centrum Wiskunde & Informatica, Netherlands

   Leiden University, Netherlands