Statistical Model Selection and its applications

这个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。另一种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的形式，如神经网络模型或小波模型。第一个目标是通过撰写一本将由Springer-Verlag出版的书《统计模型选择》来实现的。结果表明，BIC、ABIC或MDL等各种模型选择标准可以在贝叶斯框架下系统地处理。这一结果不仅将导致统计模型选择的进一步发展，而且也为目前的标准之一在选择面向计算机的模型中的容易应用提供了警示。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，AIC等模型选择准则并不适用于此类模型的选择。它不能很好地工作的原因之一是估计分布收敛到渐近分布的速度很慢，并且在参数值方面不是一致的。因此，我们探索了各种修正方法，最终发现自举类型的修正效果最好。我们还开发了一种算法来应用这种校正。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。我们开发了一种高效的算法，使比较变量和滞后的任何组合成为可能。据我们所知，当时还没有这样的软件。作为应用的结果，我们可以为不同的时间段建立一个通用的模型。

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.