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

TL;DR

This paper extends the law of the iterated logarithm to nondegenerate U-statistics derived from weakly dependent processes, such as strongly mixing data or functionals of absolutely regular processes.

Contribution

It provides new theoretical results for the law of the iterated logarithm applied to U-statistics under weak dependence conditions.

Findings

Law of the iterated logarithm established for U-statistics of weakly dependent data

Results applicable to strongly mixing processes and functionals of absolutely regular processes

Extends classical results to broader classes of dependent data

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.