Abstract
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 empirical distribution. Such statistics include density estimators and the Bahadur-Kiefer representation.
Citation
Paul Deheuvels. David M. Mason. "Functional Laws of the Iterated Logarithm for Local Empirical Processes Indexed by Sets." Ann. Probab. 22 (3) 1619 - 1661, July, 1994. https://doi.org/10.1214/aop/1176988617
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