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

ESAIM: Probability and Statistics (2009)

- Volume: 13, page 409-416
- ISSN: 1292-8100

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topKabluchko, Zakhar, and Munk, Axel. "Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays." ESAIM: Probability and Statistics 13 (2009): 409-416. <http://eudml.org/doc/250667>.

@article{Kabluchko2009,

abstract = {
We generalize a theorem of Shao [Proc. Amer. Math. Soc.123 (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 as for the multiscale signal detection.
},

author = {Kabluchko, Zakhar, Munk, Axel},

journal = {ESAIM: Probability and Statistics},

keywords = {Standardized increments; Lévy's continuity modulus; almost sure limit theorem; Erdös-Rényi law; multidimensional i.i.d. array; statistical multiscale parameter selection; scan statistics.; standardized increments; almost sure convergence; Erdős-Rényi law; multidimensional i.i.d. array},

language = {eng},

month = {9},

pages = {409-416},

publisher = {EDP Sciences},

title = {Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays},

url = {http://eudml.org/doc/250667},

volume = {13},

year = {2009},

}

TY - JOUR

AU - Kabluchko, Zakhar

AU - Munk, Axel

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

JO - ESAIM: Probability and Statistics

DA - 2009/9//

PB - EDP Sciences

VL - 13

SP - 409

EP - 416

AB -
We generalize a theorem of Shao [Proc. Amer. Math. Soc.123 (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 as for the multiscale signal detection.

LA - eng

KW - Standardized increments; Lévy's continuity modulus; almost sure limit theorem; Erdös-Rényi law; multidimensional i.i.d. array; statistical multiscale parameter selection; scan statistics.; standardized increments; almost sure convergence; Erdős-Rényi law; multidimensional i.i.d. array

UR - http://eudml.org/doc/250667

ER -

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