By Topic

Generalized form of Price's theorem and its converse

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)

The case ofnunity-variance random variablesx_{1}, x_{2},cdots, x_{n}governed by the joint probability densityw(x_{1}, x_{2}, cdots x_{n})is considered, where the density depends on the (normalized) cross-covariancesrho_{ij} = E [(x_{i}- bar{x}_{i})(x_{j} - bar{x}_{j})]. It is shown that the condition(^{ast}) frac{delta}{delta rho_{ij}}{E[f(x_{1}, x_{2}, cdots , x_{n})} = E|frac{delta^{2}}{delta x_{i} delta x_{j}}f(x_{1}, x_{2}, cdots , x_{n})| mbox{(ineq j)}holds for an "arbitrary" functionf(x_{1}, x_{2}, cdots , x_{n})ofnvariables if and only if the underlying densityw(x_{1}, x_{2}, cdots , x_{n})is the usualn-dimensional Gaussian density for correlated random variables. This result establishes a generalized form of Price's theorem in which: 1) the relevant condition(^{ast})subsumes Price's original condition; 2) the proof is accomplished without appeal to Laplace integral expansions; and 3) conditions referring to derivatives with respect to diagonal termsrho_{ij}are avoided, so that the unity variance assumption can be retained.

Published in:

Information Theory, IEEE Transactions on  (Volume:13 ,  Issue: 1 )