CMStatistics 2022: Start Registration
View Submission - CMStatistics
Title: Estimation of diffusion processes by online gradient descent Authors:  Shogo Nakakita - The University of Tokyo (Japan) [presenting]
Abstract: An online parametric estimation method is proposed for discretely observed diffusion processes via an online gradient descent algorithm. Online estimation is a classical topic in time series analysis; however, few studies discuss it in parametric estimation of stochastic differential equations under general settings. The aim is to estimate parameters in an online manner by constructing convex quasi-log-likelihood functions and optimise them via online gradient descent, whose computational complexity for each refreshment is linear with respect to the dimension of the parameter of interest. It is shown that the proposed estimator has non-asymptotic uniform risk bounds with respect to the class of stochastic differential equations, even when the model is misspecified. Our result is based on three theoretical contributions: convergence guarantee for stochastic mirror descent methods with bias and dependence; simultaneous exponential ergodicity of multidimensional diffusion processes; and proposal of loss functions and their good approximations for parametric estimation.