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Functional Laws of the Iterated Logarithm for Local Empirical Processes Indexed by Sets

Functional Laws of the Iterated Logarithm for Local Empirical Processes Indexed by Sets

We introduce the notion of a multivariate local (and tail) empirical process indexed by sets and establish a number of functionals laws of the iterated logarithm for such processes. This leads to a unified methodology to study the almost sure behavior of various statistics which are local functionals of the …