ABSTRACT
This chapter discusses the empirical likelihood (EL) ratio test with the constraints in the form of U-statistics. It first provides general explanation of U-statistics including the variance estimation. Then, it discusses the EL test statistic with U-statistic constraints. Constraints in U-statistics are not a summation of independent observations, thus the resulting EL statistic does not follow the chi-squared distribution. A correct variance needs to be incorporated into the EL statistics. This chapter discusses EL approaches for univariate and multivariate one-group and two-group U-statistics and provides some suitable examples including a multivariate rank statistic and an application to crossover designs. Relevant R codes are provided for practitioners.
