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統計数学セミナー
過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
| 担当者 | 吉田朋広、荻原哲平、小池祐太 |
|---|---|
| セミナーURL | http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/ |
| 目的 | 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. |
2017年08月23日(水)
13:30-14:40 数理科学研究科棟(駒場) 052号室
Sebastian Holtz 氏 (Humboldt University of Berlin)
Covariation estimation from noisy Gaussian observations:equivalence, efficiency and estimation
Sebastian Holtz 氏 (Humboldt University of Berlin)
Covariation estimation from noisy Gaussian observations:equivalence, efficiency and estimation
[ 講演概要 ]
In this work the estimation of functionals of the quadratic covariation matrix from a discretely observed Gaussian path on [0,1] under noise is discussed and analysed on a large scale. At first asymptotic equivalence in Le Cam's sense is established to link the initial high-frequency model to its continuous counterpart. Then sharp asymptotic lower bounds for a general class of parametric basic case models, including the fractional Brownian motion, are derived. These bounds are generalised to the nonparametric and even random parameter setup for certain special cases, e.g. Itô processes. Finally, regular sequences of spectral estimators are constructed that obey the derived efficiency statements.
In this work the estimation of functionals of the quadratic covariation matrix from a discretely observed Gaussian path on [0,1] under noise is discussed and analysed on a large scale. At first asymptotic equivalence in Le Cam's sense is established to link the initial high-frequency model to its continuous counterpart. Then sharp asymptotic lower bounds for a general class of parametric basic case models, including the fractional Brownian motion, are derived. These bounds are generalised to the nonparametric and even random parameter setup for certain special cases, e.g. Itô processes. Finally, regular sequences of spectral estimators are constructed that obey the derived efficiency statements.
