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On the Asymptotic Distribution of the Least-Squares Estimators in Unidentifiable Models

hayasaka{at}toyota-ct.ac.jp, Department of Information and Computer Engineering, Toyota National College of Technology, Toyota, Aichi 471-8525, Japan

Masashi Kitahara

kitahara{at}bpel.ics.tut.ac.jp, Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi 441–8580, Japan

Shiro Usui

usuishiro{at}riken.jp, Laboratory for Neuroinformatics, RIKEN Brain Science Institute, Wako, Saitama 351–0198, Japan

In order to analyze the stochastic property of multilayered perceptrons or other learning machines, we deal with simpler models and derive the asymptotic distribution of the least-squares estimators of their parameters. In the case where a model is unidentified, we show different results from traditional linear models: the well-known property of asymptotic normality never holds for the estimates of redundant parameters.

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