Abstract
Suppose thatB is a separable Banach space and (S,l,P) a probability space.H is a measurable symmetric kernel function fromSm intoB. In this paper we shall further study some limit theorems forB-valuedU-statisticsUmnH based onP andH. Special attention is paid upon the Marcinkiewicz type law of large numbers and the law of the iterated logarithm. Our results can be regarded as extensions of corresponding results for sums of independentB-valued random variables toU-statistics.
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