Empirical likelihood for non-degenerate U-statistics

Standard empirical likelihood for U-statistics is too computationally expensive. To overcome this computational difficulty, we reformulate the non-degenerate U-statistics as a sample mean of some “pseudo” observations in this paper, and show that the empirical log-likelihood ratio has an asymptotic chi-squared distribution under the second moment condition. The method is extremely simple to use, and yet provide better coverage accuracy in general than other alternative methods from our simulation studies.