Clustering rates and Chung type functional laws of the iterated logarithm for empirical and quantile processes

Mathematics – Statistics Theory

Scientific paper

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Scientific paper

Following the works of Berthet (1997), we first obtain exact clustering rates
in the functional law of the iterated logarithm for the uniform empirical and
quantile processes and for their increments. In a second time, we obtain
functional Chung-type limit laws for the local empirical process for a class of
target functions on the border of the Strassen set.

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