A small sample calibration method for the empirical likelihood ratio

We present a calibration method for improving the coverage accuracy of the empirical likelihood ratio confidence interval for the mean. The method is made possible by a linear transformation invariance property of its coverage level. Simulation results show that, for non-normal distributions, the coverage level of the normal distribution calibrated empirical likelihood ratio confidence interval is comparable to that of the estimated Bartlett-corrected interval. For normal distributions, its coverage level is exact and it is competitive to the t-interval in terms of the variance and expected value of the interval length.