ON THE NORMAL APPROXIMATIONS OF STUDENTIZED U-STATISTIC

抄録

The rates of convergence to a normal distribution and an Edgeworth expansion are investigated for a studentized U-statistic with arbitrary degree. In this paper we obtain an Edgeworth expansion with remainder term o(n^-1/2) and prove the validity of the expansion. We also derive an inequality which gives a lower bound of the uniform distance between two distributions of the studentized U-statistic and normal.