Empirical phi-divergence test statistics for testing simple null hypotheses based on exponentially tilted empirical likelihood estimators

TL;DR

This paper evaluates empirical phi-divergence test statistics based on exponentially tilted empirical likelihood estimators, aiming to improve robustness and accuracy in hypothesis testing under model misspecification in econometrics.

Contribution

It introduces a study of phi-divergence test statistics combined with exponential tilted empirical likelihood estimators for better robustness and efficiency in econometric hypothesis testing.

Findings

Enhanced robustness under misspecification

Improved significance level accuracy in small samples

Effective balance between efficiency and robustness

Abstract

In Econometrics, imposing restrictions without assuming underlying distributions to modelize complex realities is a valuable methodological tool. However, if a subset of restrictions were not correctly specified, the usual test-statistics for correctly specified models tend to reject erronously a simple null hypothesis. In this setting, we may say that the model suffers from misspecification. We study the behavior of empirical phi-divergence test-statistics, introduced in Balakrishnan et al. (2015), by using the exponential tilted empirical likelihood estimators of Schennach (2007), as a good compromise between efficiency of the significance level for small sample sizes and robustness under misspecification.