We prove the asymptotic normality of the two sample linear rank statistic when the independent samples arise from U-statistics with kernels of varying degree. The proof uses variance estimates of the empirical process of U-statistic structure and the continuity theorem in Denker and Rösler (1985b). This method also applies to other rank statistics. We give a sharp upper bound for the asymptotic efficacy of these statistics when the kernels are order preserving.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics