A Limit Theorem in Singular Regression Problem

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dc.creatorWatanabe, Sumio
dc.date2009-01-16
dc.date.accessioned2026-07-07T12:30:58Z
dc.date.available2026-07-07T12:30:58Z
dc.descriptionIn statistical problems, a set of parameterized probability distributions is used to estimate the true probability distribution. If Fisher information matrix at the true distribution is singular, then it has been left unknown what we can estimate about the true distribution from random samples. In this paper, we study a singular regression problem and prove a limit theorem which shows the relation between the singular regression problem and two birational invariants, a real log canonical threshold and a singular fluctuation. The obtained theorem has an important application to statistics, because it enables us to estimate the generalization error from the training error without any knowledge of the true probability distribution.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/0901.2376
dc.identifierhttp://arxiv.org/abs/0901.2376
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216298
dc.subjectMachine Learning
dc.titleA Limit Theorem in Singular Regression Problem
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