Problem of the Week
Hilton Memorial Lecture
Department of Mathematical Sciences
|DATE:||Thursday, September 28, 2017|
|TIME:||1:15pm – 2:15pm|
|SPEAKER:||Jihnhee Yu, SUNY Buffalo|
|TITLE:||Applications of empirical likelihood methods to some U-statistics|
Empirical likelihood approach with U-statistics is explained. The summands of U-statistics are not independent, and empirical weights of each summand may not have a direct interpretation as a probability point mass, dissimilar to the common empirical likelihood constraints based on independent summands. The resulting empirical likelihood ratio statistics have asymptotically weighted chi-square distributions. The proposed methods applied for some well-known U-statistics have robust Type I error control under various underlying distributions including cases with the violation of exchangeability under null hypotheses. A few applications including receiver operating characteristic curve analysis and testing in a cross-over design are presented.