Estimation for a discretely observed SPDE in two space dimensions based on temporal and spatial increments
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: asymptotic_theory
Session: IPS 689 - Asymptotic Statistics for Stochastic Ordinary and Partial Differential Equations
Wednesday 8 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)
Abstract
We consider parametric estimation for a discretely observed linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions based on temporal and spatial increments. Minimum contrast estimators (MCEs) of the unknown parameters in the SPDE are obtained by utilizing high-frequency spatio-temporal data. An approximate coordinate process is constructed from the MCEs and the spatio-temporal data. In addition, an adaptive estimator of the remaining unknown parameter in the SPDE is deduced from the temporally thinned data obtained from the approximate coordinate process. Consistency and asymptotic normality of the adaptive estimator are established. Simulation results of the proposed estimators are also provided.