AI 中文总结
研究模型误设问题，提出受微分方程约束的回归框架，利用局部多项式回归技术，聚焦局部指数增长模型，通过模拟研究比较不同估计量在两种误设场景下的表现，评估模型稳健性。
AI 中文摘要
模型误设在应用统计建模中很关键且常被视为不可避免。可通过纳入信息特征和强化模型公式来缓解，比如整合领域知识或结构约束。本文提出受微分方程约束的回归框架，利用一阶微分方程并采用局部多项式回归技术。聚焦局部指数增长模型，研究不同阶泰勒多项式构建的核估计量的渐近偏差和方差。通过模拟研究在两种误设场景下比较不同估计量来评估模型稳健性。
英文摘要
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.
