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

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作者：

机构：

[1] Kitahara, Masashi

[2] Hayasaka, Taichi

[3] Toda, Naohiro

[4] Usui, Shiro

来源：

Kitahara, M. | 1600年 / John Wiley and Sons Inc.卷 / 35期

关键词：

Error analysis - Functions - Least squares approximations - Mathematical models - Maximum likelihood estimation - Parameter estimation - Probability distributions - Regression analysis;

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摘要：

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.

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