Parameter estimation of discretely observed interacting particle systems

2022/08/25 by Amorino, Chiara, Heidari, Akram, Pilipauskaitė, Vytautė +1 · 5 citations
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2208.11965

Abstract

In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general framework, as both coefficients depend on the solution of the process and on the law of the solution itself. Starting from discrete observations of the interacting particle system over a fixed interval [0, T], we propose a contrast function based on a pseudo likelihood approach. We show that the associated estimator is consistent when the discretization step (Δ_n) and the number of particles (N) satisfy Δ_n → 0 and N → ∞, and asymptotically normal when additionally the condition Δ_n N → 0 holds.

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• Local asymptotic normality for discretely observed McKean-Vlasov diffusions
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• On goodness-of-fit testing for volatility in McKean-Vlasov models
• Dimension-Free Minimax Rates for Learning Pairwise Interactions in Attention-Style Models
• Parameter Estimation for Weakly Interacting Hypoelliptic Diffusions

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