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Laws of the iterated logarithm are established for the local U-statistic process. This entails the development of probability
inequalities and moment bounds for U-processes that should be of separate interest. The local U-statistic process is based
upon an estimator of the density of a function of several i.i.d. variables proposed by Frees (J. Am. Stat. Assoc. 89, 517–525, 1994). As a consequence, our results are directly applicable to the derivation of exact rates of uniform in bandwidth consistency
in the sup and in the L
p
norms for these estimators.
Research of E. Giné partially supported by NSA Grant H98230-04-1-0075.
Research of D.M. Mason partially supported by NSA Grant MDA904-02-1-0034 and NSF Grant DMS-0503908. 相似文献
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设X1,X2,…,Xn(n≥2)为i.i.d随机变量,Un为以h(x1,x2)为对称核的U-统计量,Eh(X1,X2)=θ,且.设是的BootstraP量,施锡铨[1]在关于核h的二阶矩的条件下,证明了:当n→∞时,因此依分布收敛于标准正态变量.本文在关于核h的4阶矩的条件下,讨论了Wn的分布渐近正态的一致性界限. 相似文献
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