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

Herold Dehling and Murad S. Taqqu

Statistics & Probability Letters, 1988, vol. 7, issue 1, 81-85

Abstract: 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.

Keywords: von; Mises; statistics; U-statistics; strong; invariance; principle; long-range; dependence; Hermite; processes (search for similar items in EconPapers)
Date: 1988
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