Displaying similar documents to “Asymptotics for products of sums and U -statistics.”

Limit theorems for rank statistics detecting gradual changes

Aleš Slabý (2001)

Commentationes Mathematicae Universitatis Carolinae

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The purpose of the paper is to investigate weak asymptotic behaviour of rank statistics proposed for detection of gradual changes, linear trends in particular. The considered statistics can be used for various test procedures. The fundaments of the proofs are formed by results of Hušková [4] and Jarušková [5].

Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays

Zakhar Kabluchko, Axel Munk (2009)

ESAIM: Probability and Statistics

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We generalize a theorem of Shao [ (1995) 575–582] on the almost-sure limiting behavior of the maximum of standardized random walk increments to multidimensional arrays of i.i.d. random variables. The main difficulty is the absence of an appropriate strong approximation result in the multidimensional setting. The multiscale statistic under consideration was used recently for the selection of the regularization parameter in a number of statistical algorithms as well...