A new method of calibration for the empirical loglikelihood ratio

Abstract

The Chi-square calibration for the empirical loglikelihood ratio refers to the method of approximating quantiles of the finite sample distribution of the empirical loglikelihood ratio with that of the limiting Chi-square distribution. Empirical likelihood ratio confidence regions are usually computed with the Chi-square calibration. Such Chi-square calibrated confidence regions can have a serious undercoverage problem. This paper examines the undercoverage problem from a finite sample standpoint and proposes a method of calibration which approximates the finite sample distributions with a new family of distributions. The new distributions is another family of sampling distributions arising from the normal distributions and is derived through a simple finite sample similarity between the empirical and parametric likelihoods. The new method of calibration is as easy to use as the Chi-square calibration. It corrects the undercoverage problem of the Chi-square calibration and is consistently more accurate.