Statistical Model Selection and its applications

这个项目有两个目的。一是建立统计模型选择的全局框架。另一种是将现有的模型选择技术扩展到可以适用于面向计算机的推理模型的形式，如神经网络模型或小波模型。第一个目标是通过写一本名为《统计模型选择》的书来实现的，这本书将由斯普林格出版社出版。结果表明，可以在贝叶斯框架中系统地处理BIC、ABIC或MDL等各种模型选择标准。这一结果不仅对统计模型选择的进一步发展具有指导意义，而且对现有的一种标准在面向计算机的模型选择中的应用提出了警告。我们还通过将注意力集中在离散观测的统计模型的选择上来进行项目。结果表明，像AIC这样的模型选择准则并不能很好地选择其中一个模型。它不能很好地工作的原因之一是渐近分布的估计分布的收敛速度很慢，并且在参数值方面不均匀。因此，我们探索了各种校正方法，最终发现自举式校正效果最好。我们还开发了一种应用这种校正的算法。我们还将统计模型选择技术应用于实际数据；7变量利率序列。我们开发了一种有效的算法，可以比较任何变量和滞后的组合。据我们所知，没有这样的软件。作为应用程序的结果，我们可以为不同的时间段建立一个公共模型。

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.