Asymptotic distributions for weighted U-statistics
Asymptotic distributions for weighted U-statistics
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加权 U 统计量的渐近分布
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
P. Major
中科院分区：
文献类型：
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作者：
P. Major
我们证明了加权U统计量的限制定理，并通过多个随机积分来表达极限。这是O'Neil和Redner对论文的概括。在该论文中，采用了时刻的方法，该方法在一般情况下不起作用。因此，我们必须解决另一种方法。特别是，在定理4中，我们描述了O'Neil和Redner提出的模型的极限。在此模型中，权重函数会引起复杂的取消，并且限制可以作为具有不同多重性的多个随机积分的总和。
We prove limit theorems for weighted U-statistics and express the limit by means of multiple stochastic integrals. This is a generalisation of the paper by O'Neil and Redner. In that paper the method of moments was applied which does not work in the general case. Hence we had to work out a different method. In particular, in Theorem 4 we describe the limit of a model proposed by O'Neil and Redner. In this model the weight functions cause an intricate cancellation, and the limit can be presented as a sum of multiple stochastic integrals with different multiplicities