2026/07/29 by Senhan Yao
Mathematics · #math.ST #stat.TH
arxiv created 2026/07/29 · arxiv updated 2026/07/30
We construct two fixed disjoint families H0,H1 of stationary ergodic binary process distributions for which a weakly asymptotically consistent test exists, but no strongly asymptotically consistent test exists. The construction combines a synchronizing binary suspension code, an independent i.i.d marker process, and countably many independent slowly switching two-state Markov chains. In particular, this disproves the asymptotic-consistency branch of a conjecture of Ryabko.