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A limit theorem in singular regression problem. (English) Zbl 1210.62102

Kotani, Motoko (ed.) et al., Probabilistic approach to geometry. Proceedings of the 1st international conference, Kyoto, Japan, 28th July – 8th August, 2008. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-931469-58-7/hbk). Advanced Studies in Pure Mathematics 57, 473-492 (2010).
The article deals with a singular regression problem, that is, one with singular Fisher information matrix, and obtains the rates of convergence of expected generalization and training errors. The results are based on resolution of singularities and depend on two birational invariants. However, the generalization error \(G\) as defined in the article is neither random, nor dependent on \(n\). So the implication of the rate of convergence of \(E[G]\) discussed in the article is not clear.
For the entire collection see [Zbl 1190.60003].

MSC:

62J99 Linear inference, regression
62E20 Asymptotic distribution theory in statistics
62H99 Multivariate analysis
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