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VOL. 5 | 2009 Gaussian integrals involving absolute value functions
Wenbo V. Li, Ang Wei

Editor(s) Christian Houdré, Vladimir Koltchinskii, David M. Mason, Magda Peligrad

Abstract

We provide general formulas to compute the expectations of absolute value and sign of Gaussian quadratic forms, i.e. $\mathbb{E}$ |〈X, AX〉+〈b, X〉+c| and $\mathbb{E}$ sgn(〈X, AX〉+〈b, X〉+c) for centered Gaussian random vector X, fixed matrix A, vector b and constant c. Products of Gaussian quadratics are also discussed and followed with several interesting applications.

Information

Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.60043
MathSciNet: MR2797939

Digital Object Identifier: 10.1214/09-IMSCOLL504

Rights: Copyright © 2009, Institute of Mathematical Statistics

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