[Paper Review] 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 Analysis0 citations

TL;DR

Introduces the Exponential-Polynomial Divergence Information Criterion (EPDIC) and the Minimum Exponential-Polynomial Divergence Estimator (MEPDE) for robust model selection in contaminated data, with tuning via generalized score matching. Applies to linear panel data models and neural networks, with influence-function analysis.

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.

Motivation & Objective

• Motivate robust model selection in the presence of contamination, outliers, and misspecification.
• 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.

Proposed method

• 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).

Experimental results

Research questions

• 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?

Key findings

• EPDIC provides a robust alternative to AIC/TIC, with an asymptotic TIC-like correction term tr(Omega Psi^{-1}).
• MEPDE is consistent and asymptotically normal under standard regularity conditions for independent non-homogeneous data.
• The influence function of EPDIC is bounded for alpha>0 and gamma>0, implying robustness to outliers; unbounded when (alpha,beta,gamma)→(0,0,0).
• GSM-based tuning parameter selection yields a data-adaptive, computationally stable approach to choose (alpha, beta, gamma) without normalizing constants.
• Simulation and real-data experiments (linear mixed-effects panel models and neural network tasks) show improved stability and reliability over classical likelihood and DPD-based criteria.