On the Statistical Properties of Regression Model Using Step-Type Basis Functions.

• Hayasaka Taichi

  Department of Information and Computer Sciences, Toyohashi University of Technology

• Hagiwara Katsuyuki

  Faculty of Electrical and Electronic Engineering, Mie University

• Toda Naohiro

  Department of Information and Computer Sciences, Toyohashi University of Technology

• Usui Shiro

  Department of Information and Computer Sciences, Toyohashi University of Technology

Bibliographic Information

Other Title

• ステップ型の基底関数を用いた回帰モデルの統計的性質について

Abstract

One of the differences between the regression models using the function representation of 3-layered neural network and the traditional linear regression models is whether the nonlinear parameters associated with the basis functions exist or not, where these parameters play a role of varying the form of the basis so as to minimize the square error. In this study, we gave attention to this feature and defined the regression model using the function representation with step-type discrete variable basis. Then we obtained the bounds of the asymptotic expectations of the least square error and the prediction square error with respect to the sample distribution using the extreme value theory. These results will provide an effective approach to the statistical properties of 3-layered neural network.

Journal

• The Brain & Neural Networks

  The Brain & Neural Networks 4 (2), 74-82, 1997

  Japanese Neural Network Society

Details

• CRID: 1390282679442007424
• NII Article ID: 10008841314
• NII Book ID: AA11658570
• DOI: 10.3902/jnns.4.74
• ISSN: 18830455
• ISSN: 1340766X
• Text Lang: ja
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed