A Minimum Distance Estimator Approach for Misspecified Ergodic Processes

TL;DR

This paper introduces a minimum distance estimator for parameter inference in misspecified ergodic processes, demonstrating its robustness and asymptotic properties, with practical implementation in Julia.

Contribution

It develops a new MDE framework for misspecified ergodic models and proves its robustness and asymptotic normality, including a numerical implementation.

Findings

Proves robustness of the MDE under model misspecification

Establishes asymptotic normality for multiscale diffusion processes

Provides a practical Julia implementation of the estimator

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.