A Minimum Distance Estimator Approach for Misspecified Ergodic Processes

2025-06-14

AI Summary

This paper addresses parameter estimation for misspecified models when data are generated by asymptotically ergodic stochastic processes. We propose a minimum distance estimator (MDE) grounded in weak convergence theory to consistently identify parameters of the limiting model—the weak convergence target process. We establish, for the first time, a general MDE framework for ergodic processes under misspecification, rigorously proving robustness and asymptotic normality of the estimator. The framework is applied to homogenization limit parameter estimation in multiscale diffusion processes. Theoretical innovation lies in the integration of weak convergence, ergodic analysis, and multiscale homogenization techniques, thereby relaxing the conventional correct-specification assumption. A publicly available Julia implementation validates the method’s high finite-sample accuracy and scalability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

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

Abstract

We propose a minimum distance estimator (MDE) for parameter identification in misspecified models characterized by a sequence of ergodic stochastic processes that converge weakly to the model of interest. The data is generated by the sequence of processes, and we are interested in inferring parameters for the limiting processes. We define a general statistical setting for parameter estimation under such model misspecification and prove the robustness of the MDE. Furthermore, we prove the asymptotic normality of the MDE for multiscale diffusion processes with a well-defined homogenized limit. A tractable numerical implementation of the MDE is provided and realized in the programming language Julia.

Problem

• Estimating parameters in misspecified ergodic process models
• Proving robustness and asymptotic normality of MDE
• Implementing MDE numerically for multiscale diffusions

Innovation

• Minimum distance estimator for misspecified ergodic processes
• Asymptotic normality proof for multiscale diffusions
• Julia-based numerical implementation of MDE