Law of the Iterated Logarithm for U-Statistics of Weakly Dependent Observations

2009/11/06 by Herold Dehling, Dehling, Herold, Martin Wendler +1
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Methods and Inference #math.PR

paper · pdf · doi:10.48550/arxiv.0911.1200

typos corrrected

openalex publication_date 2009/11/06 · arxiv created 2010/02/24 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The law of the iterated logarithm for partial sums of weakly dependent processes was intensively studied by Walter Philipp in the late 1960s and 1970s. In this paper, we aim to extend these results to nondegenerate U-statistics of data that are strongly mixing or functionals of an absolutely regular process.

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