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Statistical Model Selection and its applications

统计模型选择及其应用

基本信息

批准号：
09680315
负责人：
SHIBATA Ritei
金额：
$ 2.05万
依托单位：
Keio University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

This project has been conducted with two aims. One is to establish a global framework for statistical model selection. Another is to extend current model selection techniques to the form which can be applicable for computer oriented inference models, like neural network models or wavelet models.The first aim has been performed through writing a book "Statistical Model Selection" which will be published by Springer-Verlag. As a result, it turns out clear that various model selection criteria like BIC, ABIC or MDL can be systematically treated in a frame work of Bayesian. This result will not only lead further development of statistical model selection but also makes warning for easy application of one of currently existing criteria to the selection of a computer oriented model.We also conducted the project by concentrating our attention into the selection of statistical models for discrete observations. it is shown that model selection criterion like AIC is not good for selecting one of such models. One of reasons why it does not work well is that the speed of convergence of the distribution of estimates to the asymptotic distribution is slow and not uniform in terms of value of parameters. Therefore we explored various ways of correction and finally found that a bootstrap type correction works best. We developed an algorithm for applying this correction, too.We also applied a statistical model selection technique to a real data ; 7 variate interest rate series. We developed an efficient algorithm which makes possible to compare any combination of variables and lags. As far as we know, there was no such software. As a result of the application, we could establish a common model for various time period.

该项目的实施有两个目的。一是建立统计模型选择的全球框架。二是将现有的模型选择技术扩展到适用于面向计算机的推理模型，如神经网络模型或小波模型，第一个目标已通过编写《统计模型选择》一书实现，该书将由Springer-Verlag出版。因此，很明显，各种模型选择标准，如BIC，ABIC或MDL可以在贝叶斯框架中系统地处理。这一结果不仅将引导统计模型选择的进一步发展，而且也为将现有的一个准则简单地应用于面向计算机的模型选择提出了警告。我们还将注意力集中在离散观测的统计模型的选择上。结果表明，像AIC这样的模型选择准则对于选择这样的模型是不好的。它不能很好地工作的原因之一是估计的分布收敛到渐近分布的速度慢，并且在参数值方面不均匀。因此，我们探索了各种校正方法，最后发现自助式校正效果最好。我们也发展了一个演算法来应用这个修正，我们也将一个统计模型选择技巧应用到一个真实的数据; 7个变数的利率序列。我们开发了一种有效的算法，可以比较变量和滞后的任何组合。据我所知，没有这样的软件。应用结果表明，可以建立不同时间段的通用模型。