Abstract: In this study, we investigate the problem of testing the equality of two distributions by integrating the squared norm of the difference between two corresponding empirical characteristic functions. This results in a linear combination of three different U-statistics. Thus the original testing problem is reduced to testing whether this linear combination is zero. We apply the jackknife empirical likelihood (JEL) method to the new hypothesis testing problem. Under multivariate case, the log JEL statistic after scaling tends to a chi-square distribution with one degree of freedom. Simulation studies are presented to assess the finite-sample performance of our method.

Key words and phrases: Characteristic function, jackknife empirical likelihood, U-statistic.