statistics theory

Weak but Not Strong Asymptotic Testability

arXiv:2607.26476

summary

The paper constructs two disjoint families of stationary ergodic binary process distributions that admit a weakly asymptotically consistent test but no strongly asymptotically consistent test, thereby disproving the asymptotic‑consistency part of Ryabko’s conjecture.

Abstract

We construct two fixed disjoint families 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.

Topics & keywords

#hypothesis testing#asymptotic consistency#stationary ergodic processes#binary processes#markov chains#information theoryweak asymptotic consistencystrong asymptotic consistencysynchronizing binary suspension codei.i.d. marker processslowly switching Markov chainsRyabko conjecture
Weak but Not Strong Asymptotic Testability · wovepaper