[论文解读] An Exponential-Polynomial Divergence-based Robust Information Criterion for Linear Panel Data Models and Neural Networks

Udita Goswami, Shuvashree Mondal|arXiv (Cornell University)|Mar 25, 2026

Spatial and Panel Data Analysis被引用 0

一句话总结

提出 Exponential-Polynomial Divergence Information Criterion (EPDIC) 与 Minimum Exponential-Polynomial Divergence Estimator (MEPDE)，用于污染数据中的鲁棒模型选择，调参通过广义分数匹配进行。适用于线性面板数据模型与神经网络，并进行影响函数分析。

ABSTRACT

Model selection is a cornerstone of statistical inference, where information criteria are widely employed to balance model fit and complexity. However, classical likelihood-based criteria are often highly sensitive to contamination, outliers, and model misspecification. In this paper, we develop a robust alternative based on the Exponential-Polynomial Divergence, a flexible extension of existing divergence measures that enhances adaptability to diverse data irregularities. The proposed Exponential-Polynomial Divergence Information Criterion preserves the objective of approximating the discrepancy between the true model and candidate models while incorporating robustness against anomalous observations. Its theoretical properties are established, and robustness is examined through influence function analysis, demonstrating controlled sensitivity to extreme data points. For practical implementation, a data-driven tuning parameter selection strategy based on generalized score matching is employed, ensuring improved computational stability and efficiency. The effectiveness of the proposed method is demonstrated through extensive simulation studies under varying contamination levels, as well as real data applications involving linear mixed-effects panel data models and neural network-based prediction tasks. The results consistently show improved stability and reliability compared to classical likelihood and density power divergence-based information criteria. The proposed framework thus provides a practical and unified approach for model selection in complex and contaminated data settings.

研究动机与目标

• 在存在污染、离群点和模型 misspecification 的情况下，激发鲁棒的模型选择。
• Develop a flexible divergence-based framework that generalizes DPD, BED, and KL divergences.
• Define and analyze the Exponential-Polynomial Divergence Information Criterion (EPDIC) and its-estimator-based properties.
• Provide tuning-parameter selection via generalized score matching to ensure stability and efficiency.

提出的方法

• Define the Exponential-Polynomial Divergence (EPD) with three tuning parameters (alpha, beta, gamma) to unify several divergences (DPD, BED, KL).
• Derive the Minimum Exponential-Polynomial Divergence Estimator (MEPDE) by minimizing the empirical EPD, leading to a weighted estimating equation with weight w(t)=beta t e^{alpha t}+(1-beta)(1+gamma)t^{gamma}.
• Show that MEPDE is a robust generalization of the MDPDE for independent non-homogeneous observations and establish consistency and asymptotic normality under regularity conditions.
• Formulate the Exponential-Polynomial Divergence Information Criterion (EPDIC) as nH_n^{(alpha,beta,gamma)}( hetâ) + tr(Omega Psi^{-1}), connecting to TIC and AIC in the robust framework.
• Analyze robustness via the influence function of EPDIC, showing bounded influence for alpha>0 and gamma>0.
• Propose tuning-parameter selection via generalized score matching (GSM), minimizing the Fisher divergence to select (alpha, beta, gamma).

实验结果

研究问题

• RQ1 How to construct a robust information criterion based on Exponential-Polynomial Divergence for model selection under contamination?
• RQ2 What are the asymptotic and robustness properties (consistency, normality, influence function) of the proposed MEPDE and EPDIC?
• RQ3 How to select tuning parameters (alpha, beta, gamma) in a data-driven, stable way using GSM?
• RQ4 Do the proposed methods improve stability and reliability relative to classical likelihood-based criteria and DPD-based criteria in panel data and neural network contexts?

主要发现

• EPDIC 提供了相较于 AIC/TIC 的鲁棒替代，具有类似 TIC 的渐近修正项 tr(Omega Psi^{-1})。
• MEPDE 在独立非同质数据的标准正则条件下是一致且渐近正态的。
• EPDIC 的影响函数在 alpha>0 且 gamma>0 时是有界的，意味着对离群点具有鲁棒性；当 (alpha,beta,gamma)→(0,0,0) 时无界。
• 基于 GSM 的调参方法提供了一种数据自适应、计算上稳定的方式来选择 (alpha, beta, gamma)，且不需要归一化常数。
• 模拟和实证实验（线性混合效应面板模型与神经网络任务）显示相对于传统极大似然和基于 DPD 的准则，在稳定性与可靠性方面有所提升。