Abstract
Let be a U-statistic based on a kernel function h(x 1, x 2) and independent and identically distributed samples {X n ; n ≥ 1}. The author obtained a weak invariance principle and a strong functional limit theorem for the products of when may be infinite. Moreover, the author also applies the results to the sample variance and the Gini's mean difference, and obtain the limiting properties of their products.
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