Estimation of time series by Maximum Mean Discrepancy

2026-01-16

AI Summary

This work addresses the lack of robustness in conventional estimation methods for dynamic time series models with latent variables under model misspecification. To overcome this limitation, the authors propose a minimum distance estimator based on the Maximum Mean Discrepancy (MMD). This approach represents the first application of MMD to parameter estimation for dependent data, leveraging simulated samples to approximate the model distribution within a framework grounded in absolute regularity (β-mixing) conditions. Theoretically, the study establishes consistency and non-asymptotic convergence rates for the proposed estimator. Empirical results demonstrate that, under model misspecification, the method significantly outperforms traditional estimators, offering both robustness and computational feasibility.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When the latter one is intractable, it is approximated by simulation, allowing to accommodate most dynamic processes with latent variables. We derive the non-asymptotic and the large sample properties of our estimators in the context of absolutely regular/beta-mixing random elements. Our simulation experiments illustrate the robustness of our procedures to model misspecification, particularly in comparison with alternative standard estimation methods.

Problem

• time series
• Maximum Mean Discrepancy
• model misspecification
• latent variables
• robust estimation

Innovation

• Maximum Mean Discrepancy
• minimum distance estimation
• time series
• latent variable models
• robustness