Let be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable , where are real numbers. We derive approximate formulas for the tails and moments of X and of its decoupled version, which are exact up to some universal constants.
@article{bwmeta1.element.bwnjournal-article-smv135i1p39bwm, author = {Rafa\l\ Lata\l a}, title = {Tail and moment estimates for some types of chaos}, journal = {Studia Mathematica}, volume = {133}, year = {1999}, pages = {39-53}, zbl = {0935.60009}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv135i1p39bwm} }
Latała, Rafał. Tail and moment estimates for some types of chaos. Studia Mathematica, Tome 133 (1999) pp. 39-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv135i1p39bwm/
[00000] [1] C. Borell, Convex measures on locally convex spaces, Ark. Mat. 12 (1974), 239-252. | Zbl 0297.60004
[00001] [2] E. D. Gluskin and S. Kwapień, Tail and moment estimates for sums of independent random variables with logarithmically concave tails, Studia Math. 114 (1995), 303-309. | Zbl 0834.60050
[00002] [3] C. G. Khatri, On certain inequalities for normal distributions and their applications to simultaneous confidence bounds, Ann. Math. Statist. 38 (1967), 1853-1867. | Zbl 0155.27103
[00003] [4] R. Latała, Tail and moment estimates for sums of independent random vectors with logarithmically concave tails, Studia Math. 118 (1996), 301-304. | Zbl 0847.60031
[00004] [5] B. Maurey, Some deviation inequalities, Geom. Funct. Anal. 1 (1991), 188-197. | Zbl 0756.60018
[00005] [6] V. H. de la Peña and S. J. Montgomery-Smith, Bounds on the tail probability of U-statistics and quadratic forms, Bull. Amer. Math. Soc. 31 (1994), 223-227. | Zbl 0822.60014
[00006] [7] Z. Sidak, Rectangular confidence regions for the means of multivariate normal distributions, J. Amer. Statist. Assoc. 62 (1967), 626-633. | Zbl 0158.17705
[00007] [8] M. Talagrand, A new isoperimetric inequality and the concentration of measure phenomenon, in: Geometric Aspects of Functional Analysis (1989-90), Lecture Notes in Math. 1469, Springer, 1991, 94-124.