Session Time & Room : 1C (Aug.21, 13:20-15:00) @E504
Type : Proposal of Minisymposium
Abstract : Nowadays, a broad spectrum of large-scale and high-frequency data sets with complex spatiotemporal dependent structures is available; relevant fields of research are wide-ranging, including biology, finance, and actuarial science, to mention just a few. To create white-box models equipped with efficient and practical mechanisms for such data sets, simple combinations of the currently available devices are not enough, and it is therefore urgent and imperative to develop both mathematical statistics for stochastic processes and stochastic analyses synergistically, learning new from the past. Our session is intended to present some state-of-the-art topics in this active area of research.
[03955] Online parametric estimation of stochastic differential equations with discrete observations
Format : Talk at Waseda University
Author(s) :
Shogo Nakakita (University of Tokyo)
Abstract : We consider online parametric estimation for stochastic differential equations based on discrete observations. The proposed method uses an online gradient descent method for negative quasi-log-likelihood functions with convexity and achieves low computational complexity. We derive a non-asymptotic uniform upper bound for the risk of the estimation by our results on stochastic optimization and ergodicity.
Abstract : In this talk, we consider possibly misspecified stochastic differential equation models driven by L\'{e}vy processes. Under some regularity conditions, Gaussian quasi-likelihood estimator can estimate unknown parameters in the drift and scale coefficients. However, especially in the misspecified case, it is hard to construct a consistent estimator of the asymptotic variance directly. For such a problem, we propose a weighted block bootstrap procedure to evaluate the asymptotic distribution.
[04399] Robustifying Gaussian quasi-likelihood inference for random dynamics
Format : Talk at Waseda University
Author(s) :
Shoichi Eguchi (Osaka Institute of Technology)
Abstract : We consider Gaussian quasi-likelihood inference for stochastic differential equations. In this study, suppose that the observations are obtained from the L\'{e}vy process with the compound-Poisson jumps and spike noises, and we regard jumps and spike noises as outliers that disturb the parameter estimation. We construct an estimator without reference to the presence of the jump component and some spike noises, in addition to that of the drift term.
[04695] Asymptotic expansion of estimator of Hurst parameter of SDE driven by fractional Brownian motion
Format : Talk at Waseda University
Author(s) :
Hayate Yamagishi (University of Tokyo)
Abstract : Asymptotic expansion is presented for an estimator of the Hurst coefficient of a stochastic differential equation driven by a fractional Brownian motion of H>1/2. While applying a recently developed theory of asymptotic expansion of Wiener functionals to the estimator, the main difficulty is to estimate orders of complicated functionals appearing in expanding the estimator and identifying the limit random symbols. To overcome the difficulty, we introduce a theory of an exponent based on weighted graphs.
