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VOL. 57 | 2010 A limit theorem in singular regression problem
Sumio Watanabe

Editor(s) Motoko Kotani, Masanori Hino, Takashi Kumagai


In statistical problems, a set of parameterized probability distributions is often used to estimate the true probability distribution. If the 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 accuracy of singular regression 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.


Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1210.62102
MathSciNet: MR2648274

Digital Object Identifier: 10.2969/aspm/05710473

Primary: 60D05

Rights: Copyright © 2010 Mathematical Society of Japan


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