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Seminar on Probability and Statistics
Seminar information archive ～05/02｜Next seminar｜Future seminars 05/03～
| Organizer(s) | Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike |
|---|
2007/01/17
16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
玉置 健一郎 (早稲田大学)
Second order optimality for estimators in time series regression models
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/17.html
玉置 健一郎 (早稲田大学)
Second order optimality for estimators in time series regression models
[ Abstract ]
We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator $\\hat{\\beta}$ proposed by Hannan (1963). This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of $\\hat{\\beta}$. Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that $\\hat{\\beta}$ has the same rate of convergence as in regular parametric estimation. This is a sharp contrast with the general semiparametric estimation theory. We also examine the second order Gaussian efficiency of $\\hat{\\beta}$. Numerical studies are given to confirm the theoretical results.
[ Reference URL ]We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator $\\hat{\\beta}$ proposed by Hannan (1963). This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of $\\hat{\\beta}$. Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that $\\hat{\\beta}$ has the same rate of convergence as in regular parametric estimation. This is a sharp contrast with the general semiparametric estimation theory. We also examine the second order Gaussian efficiency of $\\hat{\\beta}$. Numerical studies are given to confirm the theoretical results.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/17.html
