Convergence Rates of Two Sample U -Statistics in Non IID Case

An estimate of the remainder of two sample U-statistics where each sample consists of independent observations, from its linear projection is obtained. A Berry-Esseen theorem with random index is established. A normal approximation zone for the tail probability of a standardized U-statistic is obtained. Application of this statistic to a real data set related to burr formation in production processes is investigated as a nonparametric tool, instead of a model based approach.