Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Order-of-Magnitude Bounds for Expectations Involving Quadratic Forms

Victor H. de la Pena and Michael J. Klass
The Annals of Probability
Vol. 22, No. 2 (Apr., 1994), pp. 1044-1077
Stable URL: http://www.jstor.org/stable/2244904
Page Count: 34
Preview not available

Abstract

Let X1, X2,...,Xn be independent mean-zero random variables and let aij, 1 ≤ i, j ≤ n, be an array of constants with $a_{ii} \equiv 0$. We present a method of obtaining the order of magnitude of EΦ(∑1≤ i,j≤ naijXiX j) for any such {Xi} and {aij} and any nonnegative symmetric (convex) function Φ with Φ(0) = 0 such that, for some integer k ≥ 0, Φ(x2-k) is convex and simultaneously Φ(x2-k-1 ) is concave on [ 0, ∞). The approximation is based on decoupling inequalities valid for all such mean-zero {Xi} and reals {aij} and a certain further "independentization" procedure.

• 1044
• 1045
• 1046
• 1047
• 1048
• 1049
• 1050
• 1051
• 1052
• 1053
• 1054
• 1055
• 1056
• 1057
• 1058
• 1059
• 1060
• 1061
• 1062
• 1063
• 1064
• 1065
• 1066
• 1067
• 1068
• 1069
• 1070
• 1071
• 1072
• 1073
• 1074
• 1075
• 1076
• 1077