1998 Fiscal Year Final Research Report Summary
Statistical Model Selection and its applications
| Project/Area Number |
09680315
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Keio University |
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Principal Investigator |
SHIBATA Ritei Keio Univ, Dept.Math.Professor, 理工学部, 教授 (60089828)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Statistical Model / Model Selection / Bootstrap / Neurul Network / Multivariate AR / GARCH model / Validation |
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| Research Abstract |
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.
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