2010 Fiscal Year Final Research Report
A study on statistical theory of choosing a smoothing parameter for spectral density estimation and its application
| Project/Area Number |
20500248
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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 | Hokkaido University |
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Principal Investigator |
KAKIZAWA Yoshihide Hokkaido University, 大学院・経済学研究科, 准教授 (30281778)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 定常過程 / スペクトル密度 / ノンパラメトリック推定 |
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| Research Abstract |
The smoothing parameter in nonparametric function estimation plays a role in controlling the trade off between the approximation error (in terminology of Statistics, it is nothing but bias of the estimator) and variance of the estimator. In this research, I discussed a new spectral density estimator/probability density estimator based on a generalized Bernstein polynomial approximation theory, in which the degree of polynomial and the additional second parameter are the smoothing parameters. Especially, main focus is the selection problem of these two parameters, where the latter second parameter enables us to generalize the classical Bernstein method. I established several formulas of asymptotic bias, variance and mean squared error as well as the asymptotic normality of the proposal.
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