A0474
Title: Parameter estimation for weakly interacting hypoelliptic diffusions
Authors: Yuga Iguchi - Lancaster University (United Kingdom) [presenting]
Alexandros Beskos - University College London (United Kingdom)
Greg Pavliotis - Imperial College London (United Kingdom)
Abstract: Parameter estimation is studied for an $N$-weakly interacting particle system (IPS) of multidimensional hypo-elliptic SDEs, where each particle is typically characterized by a degenerate diffusion matrix. A locally Gaussian approximation is proposed, carefully designed to address the degenerate structure, which provides an approximate joint transition density and thus forms a tractable full likelihood, enabling statistical inference for a wider class of hypo-elliptic IPSs that are not covered by a recent work relying on a locally degenerate approximation, specifically the Euler-Maruyama method. A contrast estimator is then analyzed, based on the likelihood from $n$ discretely sampled particle observations with a fixed time interval $T$, and its asymptotic normality is shown as $n, N \to \infty$ with a requirement on the step-size $\Delta_n \equiv T/n = o (1/N)$, assuming all particle coordinates are observed. In practical situations where only partial coordinates of particle trajectories are observed, the proposed locally Gaussian approximation offers greater flexibility in inference combined with standard computational statistics methodologies, compared to the Euler-Maruyama type estimator that requires a particular structure for the hypo-elliptic model. Numerical experiments that illustrate the effectiveness of using the locally Gaussian approximation-based likelihood are presented in settings where complete or partial particle trajectories are observed.
