Differential Equation-Constrained Exponential-Type Local Polynomial Regression Under Model Misspecification

2026-07-27

AI Summary

This study addresses estimation bias arising from model misspecification in statistical modeling by proposing a local polynomial regression framework that incorporates first-order differential equation constraints—specifically, exponential growth structures. The method innovatively integrates differential equation priors into local kernel estimation, constructing estimators via Taylor expansions of varying orders to substantially enhance the robustness of local regression under model misspecification. A rigorous theoretical analysis characterizes the asymptotic bias and variance properties of the proposed estimator. Extensive simulations demonstrate its superior performance over conventional approaches across multiple misspecification scenarios, achieving both higher accuracy and improved robustness.

Abstract

The issue of model misspecification is critical, yet it is often regarded as unavoidable in applied statistical modeling. Model misspecification can be mitigated by incorporating informative features and strengthening model formulations, such as through the integration of domain knowledge or structural constraints. In this paper, we propose a regression framework constrained by differential equations, which leverages first-order differential equations and adapts local polynomial regression techniques. Specifically, we focus on the local exponential growth model, characterized by an exponential-type differential equation. For this model, we examine the asymptotic biases and variances of kernel estimators constructed using Taylor polynomials of varying degrees. To evaluate model robustness, we conduct simulation studies comparing different estimators under two misspecification scenarios varying the levels of misspecification.

Problem

• model misspecification
• differential equation constraints
• local polynomial regression
• exponential-type model
• robustness

Innovation

• differential equation constraints
• local polynomial regression
• model misspecification
• exponential-type model
• kernel estimators