Abstract: This paper is concerned with inference for the population quantile difference (e.g., the interquartile range). Although normal approximations could be used for this purpose, they usually give poor performances unless the sample size is sufficiently large. In this paper, we investigate the use of the nonparametric likelihood method. Numerical results will be presented to compare its performance with other methods.
Key words and phrases: Bandwidth, confidence interval, quantile difference, smoothed empirical likelihood.