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A complete characterization of sequential testability and change detectability in i.i.d. models — arXiv:2609.05752

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.05752
License (as archived): CC0-1.0
Archived: 2026-10-16T14:09:32.909Z
SHA-256 of the archived text: 97e9af321fc58338798196a3e5c2563f479b537e09446bc0b3e9ce12b157bc71
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How to cite

A complete characterization of sequential testability and change detectability in i.i.d. models — arXiv:2609.05752 — arXiv (en), https://arxiv.org/abs/2609.05752 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_586e523dc5d6 (Metraipolis archive dc_586e523dc5d6, sha256 97e9af321fc58338798196a3e5c2563f479b537e09446bc0b3e9ce12b157bc71)

BibTeX

@misc{dc586e523dc5d6,
  title = {A complete characterization of sequential testability and change detectability in i.i.d. models — arXiv:2609.05752},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.05752},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_586e523dc5d6; sha256 97e9af321fc58338798196a3e5c2563f479b537e09446bc0b3e9ce12b157bc71},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.05752. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We give a necessary and sufficient condition for the existence of power-one sequential tests in an i.i.d. composite testing problem. A level-\(\alpha\) test with power one against every alternative exists if and only if the alternatives are separated from the null by a countable family of finite-block events. We provide other equivalent conditions using randomized fixed-sample tests, bounded finite-block scores, e-processes, reduced-filtration test supermartingales, and a countable cover whose finite-block weak-$*$ closed convex hulls are positively separated in total variation. As a bonus, the constructive proof yields tests have pointwise expected sample size \(O_Q(\log(1/\alpha))\). Exactly the same conditions also characterize i.i.d.\ change detectability under optional-horizon average-run-length control: for every \(\eta>0\), they are equivalent to an alarm family \((T_\gamma)_{\gamma\ge1}\) satisfying \(\Prob_{P^\infty}(T_\gamma\le\sigma)\le \E_{P^\infty}\sigma/\gamma\) for every null law and every stopping time \(\sigma\). In fact, when these conditions hold, we can construct a single e-detector such that every null-law average run length lies between \(\gamma\) and \((1+\eta)\gamma+1\), and having robust Lorden delay \(O_Q(\log\gamma)\).

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-09 in stat.ML).
Categorie arXiv: Statistics Theory (math.ST) ; Information Theory (cs.IT); Signal Processing (eess.SP); Methodology (stat.ME); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2609.05752 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T13:59:13.703Z dalla pagina https://arxiv.org/catchup/stat.ML/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).