On the statistical properties of least-square estimators of layered neural networks

  • Authors:

  • Masashi Kitahara;Taichi Hayasaka;Naohiro Toda;Shiro Usui

  • Affiliations:

  • Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, 441-8580 Japan;Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, 441-8580 Japan;Department of Applied Information Science and Technology, Aichi Prefectural University, Aichi, 480-1198 Japan;Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, 441-8580 Japan

  • Venue:
  • Systems and Computers in Japan
  • Year:
  • 2004

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Abstract

There are still some statistical properties which have not been clarified in the regression model based on the three-layered neural network. This paper presents an analysis of these problems, in terms of the probability distribution of the parameter estimators. It is first shown numerically that the least-square estimator for the condition in which the probability distribution for the parameter estimator has not been clearly described follows a distribution which is different from the probability distribution derived in the past for various conditions. Based on the result, a theoretical analysis is presented for the simplified regression model, and it is shown that the least-square parameter estimator follows the double-exponential distribution. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(12): 1–9, 2004; Published online in Wiley InterScience (). DOI 10.1002/scj.10580