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日仏数学拠点FJ-LMIセミナー
過去の記録 ～05/01｜次回の予定｜今後の予定 05/02～
| 担当者 | 小林俊行, ミカエル ペブズナー |
|---|
2025年04月23日(水)
13:30-14:15 数理科学研究科棟(駒場) 056号室
Alexandre BROUSTE 氏 (Le Mans Université)
Fast and efficient inference for large and high-frequency data (英語)
https://fj-lmi.cnrs.fr/seminars/
Alexandre BROUSTE 氏 (Le Mans Université)
Fast and efficient inference for large and high-frequency data (英語)
[ 講演概要 ]
The theory of Local Asymptotic Normality (LAN), initiated by Lucien Le Cam, provides a powerful framework for studying the asymptotic optimality of estimators. When the LAN property holds for a statistical experiment with a non-singular Fisher information matrix, minimax theorems can be applied, allowing for the derivation of a lower bound for the variance of estimators.
Beyond the classical i.i.d. setting, the LAN property has been established for various statistical models. However, for several high-frequency statistical experiments, only weak LAN properties were derived with a singular Fisher information matrix, preventing the application of minimax theorems. For these experiments, it has also remained unclear for a long time whether the maximum likelihood estimator (MLE) possesses any form of asymptotic optimality.
Moreover, when the MLE achieves optimality, its computation is generally time-consuming, making it challenging for handling large or high-frequency datasets and alternative estimation methods are therefore needed for different applications.
In this talk, we review our previous results obtained with M. Fukasawa on fractional Gaussian noise and H. Masuda on stable processes observed at high frequency as well as the various progress made since then. We also present our efforts to popularize the one-step procedure as a fast and asymptotically efficient alternative to the MLE.
[ 講演参考URL ]The theory of Local Asymptotic Normality (LAN), initiated by Lucien Le Cam, provides a powerful framework for studying the asymptotic optimality of estimators. When the LAN property holds for a statistical experiment with a non-singular Fisher information matrix, minimax theorems can be applied, allowing for the derivation of a lower bound for the variance of estimators.
Beyond the classical i.i.d. setting, the LAN property has been established for various statistical models. However, for several high-frequency statistical experiments, only weak LAN properties were derived with a singular Fisher information matrix, preventing the application of minimax theorems. For these experiments, it has also remained unclear for a long time whether the maximum likelihood estimator (MLE) possesses any form of asymptotic optimality.
Moreover, when the MLE achieves optimality, its computation is generally time-consuming, making it challenging for handling large or high-frequency datasets and alternative estimation methods are therefore needed for different applications.
In this talk, we review our previous results obtained with M. Fukasawa on fractional Gaussian noise and H. Masuda on stable processes observed at high frequency as well as the various progress made since then. We also present our efforts to popularize the one-step procedure as a fast and asymptotically efficient alternative to the MLE.
https://fj-lmi.cnrs.fr/seminars/
