2024/09/17 by Yunda Hao, Peter Grünwald, Hao, Yunda +1 · 1 citation
Engineering · #FOS: Computer and information sciences #ICT Impact and Policies #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.2409.11134
openalex publication_date 2024/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze common types of e-variables and e-processes for composite exponential family nulls: the optimal e-variable based on the reverse information projection (RIPr), the conditional (COND) e-variable, and the universal inference (UI) and sequen\-tialized RIPr e-processes. We characterize the RIPr prior for simple and Bayes-mixture based alternatives, either precisely (for Gaussian nulls and alternatives) or in an approximate sense (general exponential families). We provide conditions under which the RIPr e-variable is (again exactly vs. approximately) equal to the COND e-variable. Based on these and other interrelations which we establish, we determine the e-power of the four e-statistics as a function of sample size, exactly for Gaussian and up to o(1) in general. For d-dimensional null and alternative, the e-power of UI tends to be smaller by a term of (d/2) log n + O(1) than that of the COND e-variable, which is the clear winner.