Standard Curves for Empirical Likelihood Ratio Tests of Means

TL;DR

This paper provides simulated standard curves to calibrate empirical likelihood ratio tests of means, enabling more accurate significance level adjustments for finite samples based on distribution skewness and kurtosis.

Contribution

It introduces a method to adjust ELR test significance levels using simulated standard curves, accounting for distribution skewness and kurtosis.

Findings

Adjusted significance levels depend on skewness and kurtosis.

Tabulated critical values for common models.

Enhanced control of type I error rates.

Abstract

We present simulated standard curves for the calibration of empirical likelihood ratio (ELR) tests of means. With the help of these curves, the nominal significance level of the ELR test can be adjusted in order to achieve (quasi-) exact type I error rate control for a given, finite sample size. By theoretical considerations and by computer simulations, we demonstrate that the adjusted significance level depends most crucially on the skewness and on the kurtosis of the parent distribution. For practical purposes, we tabulate adjusted critical values under several prototypical statistical models.