@article{JakubOnufryWojtaszczyk2009,
abstract = {Negative association for a family of random variables $(X_i)$ means that for any coordinatewise increasing functions f,g we have
$ (X_\{i₁\},...,X_\{i_k\}) g(X_\{j₁\},...,X_\{j_l\}) ≤ f(X_\{i₁\},...,X_\{i_k\}) g(X_\{j₁\},...,X_\{j_l\})$
for any disjoint sets of indices (iₘ), (jₙ). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics by Alem Saxena and Joag-Dev Proschan, and brought to convex geometry in 2005 by Wojtaszczyk Pilipczuk to prove the Central Limit Theorem for Orlicz balls. The paper gives a relatively simple proof of negative association of absolute values for a wide class of measures tied to generalized Orlicz balls, including the uniform measures on such balls.},
author = {Jakub Onufry Wojtaszczyk},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {negative association; Orlicz balls; central limit theorem; log-concave measure},
language = {eng},
number = {1},
pages = {41-56},
title = {A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls},
url = {http://eudml.org/doc/281206},
volume = {57},
year = {2009},
}
TY - JOUR
AU - Jakub Onufry Wojtaszczyk
TI - A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2009
VL - 57
IS - 1
SP - 41
EP - 56
AB - Negative association for a family of random variables $(X_i)$ means that for any coordinatewise increasing functions f,g we have
$ (X_{i₁},...,X_{i_k}) g(X_{j₁},...,X_{j_l}) ≤ f(X_{i₁},...,X_{i_k}) g(X_{j₁},...,X_{j_l})$
for any disjoint sets of indices (iₘ), (jₙ). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics by Alem Saxena and Joag-Dev Proschan, and brought to convex geometry in 2005 by Wojtaszczyk Pilipczuk to prove the Central Limit Theorem for Orlicz balls. The paper gives a relatively simple proof of negative association of absolute values for a wide class of measures tied to generalized Orlicz balls, including the uniform measures on such balls.
LA - eng
KW - negative association; Orlicz balls; central limit theorem; log-concave measure
UR - http://eudml.org/doc/281206
ER -
