Hoeffding spaces and Specht modules

Giovanni Peccati; Jean-Renaud Pycke

ESAIM: Probability and Statistics (2011)

  • Volume: 15, page S58-S68
  • ISSN: 1292-8100

Abstract

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It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.

How to cite

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Peccati, Giovanni, and Pycke, Jean-Renaud. "Hoeffding spaces and Specht modules." ESAIM: Probability and Statistics 15 (2011): S58-S68. <http://eudml.org/doc/277134>.

@article{Peccati2011,
abstract = {It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.},
author = {Peccati, Giovanni, Pycke, Jean-Renaud},
journal = {ESAIM: Probability and Statistics},
keywords = {exchangeability; finite population statistics; Hoeffding decompositions; irreducible representations; random permutations; Specht modules; symmetric group},
language = {eng},
pages = {S58-S68},
publisher = {EDP-Sciences},
title = {Hoeffding spaces and Specht modules},
url = {http://eudml.org/doc/277134},
volume = {15},
year = {2011},
}

TY - JOUR
AU - Peccati, Giovanni
AU - Pycke, Jean-Renaud
TI - Hoeffding spaces and Specht modules
JO - ESAIM: Probability and Statistics
PY - 2011
PB - EDP-Sciences
VL - 15
SP - S58
EP - S68
AB - It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.
LA - eng
KW - exchangeability; finite population statistics; Hoeffding decompositions; irreducible representations; random permutations; Specht modules; symmetric group
UR - http://eudml.org/doc/277134
ER -

References

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  9. [9] G. Peccati, Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations. Ann. Probab.32 (2004) 1796–1829. Zbl1055.62060MR2073178
  10. [10] G. Peccati and J.-R. Pycke, Decompositions of stochastic processes based on irreducible group representations. Theory Probab. Appl.54 (2010) 217–245. Zbl1229.60039MR2761557
  11. [11] B.E. Sagan, The Symmetric Group. Representations, Combinatorial Algorithms and Symmetric Functions, 2nd edition. Springer, New York (2001). Zbl0964.05070MR1824028
  12. [12] R.J. Serfling, Approximation Theorems of Mathematical Statistics. Wiley, New York (1980). Zbl1001.62005MR595165
  13. [13] J.-P. Serre, Linear representations of finite groups, Graduate Texts Math. 42, Springer, New York (1977). Zbl0355.20006MR450380
  14. [14] L. Zhao and X. Chen, Normal approximation for finite-population U-statistics. Acta Math. Appl. Sinica6 (1990) 263–272. Zbl0724.60024MR1078067

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