Séminaire_21_novembre

ANR EFFI France-Japan seminar

Le 21 novembre 2022

As part of the ANR 2022-2025 project "Efficient inference for large and high-frequency data", the second seminar will be held both online and in presential, starting Monday November 21st, 2022 from 9:15 a.m. to 11:30 a.m. (Paris time). 

Program:

9h15-10h15, Yury Kutoyants, Le Mans University, Parameter estimation of hidden Markov processes and adaptive filtration. Ergodic case.

Abstract: We are given a linear partially observed system depending of some unknown parameters and study the method of moments estimators, MLE, Bayesian estimators and One-step MLE. The cases of one-dimensional and two-dimensional  parameters are considered separately. Then these estimators are used for the construction of adaptive filter of unobserved component. The properties of estimators and of adaptive filter are described in the asymptotics of large samples.

10h30-11h30, Tetsuya Takabatake, Hiroshima University, Asymptotically Efficient Estimation for Fractional Brownian Motion with Additive Noise

Abstract: In this presentation, we will talk about a local asymptotic normality property for a fractional Brownian motion with additive noise, including a mixed fractional Brownian motion, based on discrete observations. Moreover, we will also talk about our recent progress of asymptotically efficient estimation of the Hurst index and the volatility parameters for the fractional Brownian motion and the additive noise. Our proposed estimator is based on combining ideas of a one-step estimator and a quadratic variation-type estimator with pre-averaged data. This talk is based on a joint work with Grégoire Szymanski at École Polytechnique and Université Paris Dauphine-PSL.