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Anytime-valid t-tests and confidence sequences for Gaussian means with unknown variance
April 25, 2024, 7:43 p.m. | Hongjian Wang, Aaditya Ramdas
cs.LG updates on arXiv.org arxiv.org
Abstract: In 1976, Lai constructed a nontrivial confidence sequence for the mean $\mu$ of a Gaussian distribution with unknown variance $\sigma^2$. Curiously, he employed both an improper (right Haar) mixture over $\sigma$ and an improper (flat) mixture over $\mu$. Here, we elaborate carefully on the details of his construction, which use generalized nonintegrable martingales and an extended Ville's inequality. While this does yield a sequential t-test, it does not yield an "e-process" (due to the nonintegrability …
abstract arxiv confidence cs.lg distribution flat math.st mean stat.me stat.ml stat.th tests type variance
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