| Standard empirical likelihood for U-statistics is too computationally expensive due to the nonlinear constraint in the underlying optimization problem. To sidestep this difficult computational issue, the pseudo-values empirical likelihood method is proposed in this thesis. Motivated by the fact that the jackknife pseudo-values are asymptotically independent and identically distributed, we apply the standard empirical likelihood to the mean functional based on these jackknife pseudo-values although they are dependent in general. Wilks's theorem is shown under the second moment condition, which may be used to construct confidence intervals or do hypothesis testing.;This method of combining jackknife and empirical likelihood could work more generally than just for U-statistics. We also make an attempt to apply the pseudo-values empirical likelihood to generalized U-statistics. Wilks's theorem is shown to hold under mild conditions after a long mathematical proof. The pseudo-values empirical likelihood for two sample U-statistics is extremely simple to use, and yet has very good coverage properties from our simulation study. As applications, we make statistical inference about P(X < Y), the so-called stress-strength model, and study the efficiency of different diagnostic markers via comparing the areas under the ROC curves of markers. |
