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Accomplishment Based Renewal For Research in Specification Testing, Nonparametric Estimation and Neural Networks

规范测试、非参数估计和神经网络研究的基于成就的更新

基本信息

批准号：
9209023
负责人：
Halbert White
金额：
$ 16.03万
依托单位：
University of California-San Diego
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
1992
资助国家：
美国
起止时间：
1992-07-15 至 1996-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9209023&HistoricalAwards=false
关键词：
Accomplishment Based Renewal Research Specification

项目摘要

Artificial neural networks (ANN's) are a rich and interesting class of nonlinear models developed recently by cognitive scientists. Although inspired by certain features of the neural architecture of the brain, these models have considerable potential for use in econometrics and economics because of their simplicity and great flexibility. Specifically, ANN models show promise as the basis for nonparmetric estimation and for specification testing because of their ability to approximate arbitrary elements of general function spaces to arbitrary accuracy. Under previous NSF grants, this project focused on establishing the mathematical and statistical foundations necessary for using ANN models in nonparametric estimation and specification testing. The research proposed in this accomplishment based renewal is to continue development of these foundations, to establish properties of ANN- based nonparametric estimators, and to apply the resulting theory to construct model specification tests. The areas in which mathematical and statistical theory will be pursued are two. The first area is the establishment of degree of approximation results for ANN models in Sobolev spaces. The second area is to obtain central limit theorems and invariance principles for random elements constructed as partial sums of a dependent process (specifically, a mixingale process) in a Hilbert space. The application areas make direct use of the proposed theoretical results to model learning by economic agents.

人工神经网络（ANN）是一个丰富而有趣的类认知科学家最近开发的非线性模型。尽管受到神经结构某些特征的启发这些模型具有相当大的潜力，可用于计量经济学和经济学，因为它们的简单性和伟大的灵活性. 具体来说，人工神经网络模型显示承诺作为基础，对于非参数估计和规格检验，他们的能力，以近似任意元素的一般函数空间到任意精度。在以前的NSF赠款下，该项目的重点是建立数学和使用ANN模型所需的统计基础非参数估计和规范测试。研究在这一基于成绩的更新中，这些基础的发展，建立ANN的属性- 的非参数估计，并应用所得理论构建模型规格测试。数学和统计理论将被追求是两个。第一个方面是建立程度 Sobolev空间中的ANN模型的近似结果。第二面积是获得中心极限定理和不变性原理对于构造为相依函数的部分和的随机元，过程（特别是混合过程）。应用领域直接使用所提出的理论结果来模拟经济主体的学习。