We obtain the H-decomposition of a jackknife estimator of the variance of U-statistic and derive an Edgeworth expansion with remainder term o(n 12). We also obtain an approximation of a studentized U-statistic substituting the jackknife estimator of the variance. An Edgeworth expansion with remainder term o(n-1) is established for the studentized U-statistic with arbitrary degree of the kernel.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics