6 juin 2023

ANR EFFI France-Japan seminar

Le 6 juin 2023

As part of the ANR 2022-2025 project "Efficient inference for large and high-frequency data", the third seminar will be held both online and in presential, starting Tuesday June 6th, 2023 from 9:15 a.m. to 11:30 a.m. (Paris time). 

Program:

9h15-10h15, Hiroki Masuda, Tokyo University, Consistent model selection for locally stable trend-scale regression.

Abstract: The locally stable regression model has three primary characteristics: trend, scale, and activity index. In this talk, we are interested in consistent model selection criteria for the first two elements. Under suitable conditions, we may regard the tail area of the driving Levy measure as a nuisance element, with or without ergodicity.

10h30-11h30, Laurent Denis, Le Mans Université, LAMN for Euler scheme of SDE driven by stable Lévy processes

Abstract: We study the stochastic differential equations driven by a symmetric stable Lévy process, in which the joint parametric estimation of the drift coefficient, the scale coefficient and the jump activity of the process based on high frequency observations on a fixed time interval is considered. For these experiments, due to the non-explicit form of the likelihood function, our methodology will be to identify a simpler experiment, where the likelihood function has a traceable form, which is asymptotically equivalent in the Le Cam distance at the process observed at high frequency. To cover all values of jumping activity, the most appropriate experiment is to consider a numerical scheme that combines Euler's approximation of the scale coefficient with the solution of the ordinary equation given by the coefficient of derivative. We therefore prove the LAMN property for this corresponding Euler scheme with the ordinary differential equation. Thanks to the obtained LAMN property, we show that the one-step estimator is efficient. With an easy-to-compute initial estimator with good asymptotic behavior, it can exhibit a performance quite similar to that of the maximum likelihood estimator and reduce a lot of computation time. We illustrate our results by numerical simulations with the one-step procedure.