The functional law of the iterated logarithm for the empirical process of some long-range dependent sequences

Let (Xi)[infinity]i = 1 be a stationary, mean-zero Gaussian process with covariances r(k) = EXk + 1 X1 satisfying r(0) = 1 and r(k) = k-DL(k). Consider the two-parameter empirical process for G(Xi), where G is any measurable function. The Functional Law of the Iterated Logarithm as well as a Strong Invariance Principle are obtained for FN(x,t). Applications to U-statistics and von Mises statistics are given.

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Year of publication:	1988
Authors:	Dehling, Herold ; Taqqu, Murad S.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 7.1988, 1, p. 81-85
Publisher:	Elsevier
Keywords:	von Mises statistics U-statistics strong invariance principle long-range dependence Hermite processes

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005254865