Cressie Read Power Divergence for Moment-Based Estimation: Hyperparameter and Finite Sample Behavior

TL;DR

This paper investigates how the choice of the hyperparameter in Cressie Read power divergence estimation affects finite sample performance, robustness, and bias, providing guidance for optimal tuning in moment-based models.

Contribution

It interprets the power parameter as a hyperparameter influencing estimator behavior and offers second order asymptotic analysis and simulations for optimal tuning.

Findings

The power parameter impacts robustness, bias, and sensitivity.

Monte Carlo simulations show performance varies with the hyperparameter.

Empirical example demonstrates practical importance of tuning the parameter.

Abstract

We study Cressie Read power divergence (CRPD) estimation for moment based models, focusing on finite sample behavior. While generalized empirical likelihood estimators, dual to CRPD, are known to outperform generalized method of moments estimators in small to moderate samples, the power parameter is typically chosen arbitrarily by the researcher, serving mainly as an index. We interpret it as a hyperparameter that determines the loss function and governs the learning procedure, shaping the curvature of the objective and influencing finite sample performance. Using second order asymptotics, we show that it affects both the structural estimator and the associated Lagrange multipliers, governing robustness, bias, and sensitivity to sampling variation. Monte Carlo simulations illustrate how estimator performance varies with the choice of the power parameter and underlying distributional features, with implications for second order bias and coverage distortion. An empirical illustration based on Owen (2001)s classical example highlights the practical relevance of tuning the power parameter.