## 統計数学セミナー

担当者 吉田朋広、荻原哲平、小池祐太 http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/ 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う.

### 2007年01月17日(水)

16:20-17:30   数理科学研究科棟(駒場) 128号室

Second order optimality for estimators in time series regression models
[ 講演概要 ]
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.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/17.html