On the statistical properties of least‐square estimators of layered neural networks
Masashi Kitahara, Taichi Hayasaka, Naohiro Toda, Shiro Usui · Systems and Computers in Japan · 2004
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 ( www.interscience.wiley.com ). DOI 10.1002/scj.10580