Abstract: How statistical and mathematical tools commonly used independently can advantageously be exploited together was studied in order to improve neural network estimation and selection in nonlinear static modeling. The statistical tools considered were the analysis of the numerical conditioning of the neural network candidates, statistical hypothesis tests, and cross validation. Each of these tools was presented and analyzed in order to justify at what stage of a construction and selection procedure they can be most useful. On the basis of this analysis, a novel and systematic construction and selection procedure for neural modeling was proposed. In the end, its efficiency was illustrated through simulations.

Key words: neural networks, model selection, statistical hypothesis tests

摘要： 主要研究了如何将平时单独使用的数学方法和统计学方法根据它们各自的优点综合运用,以提高非线性建模过程中神经网络模型构建和选择的效率。所使用的统计学工具包括矩阵的条件数,假设检验,交叉验证。文中对每个方法进行综合分析,进而判断它们分别应用在神经网络模型构建与选择过程的哪个阶段是最有效的。在此基础上,提出了一个系统的神经网络模型的构建与选择程序,并最终通过仿真试验来说明这个程序的有效性。

关键词: 神经网络, 模型选择, 统计检验