The curvature induced by covariance

The objective of the paper is to construct the signed measure which is the closest one to independence subject to given cavariances between random variables, where closeness is measured by using Pearson's [chi]2 indicator. The difference between this signed measure and the independent, direct product of the marginals gives the curvature induced by the linear dependence between random variables. The signed measure may be extended to the sample space of a time series and used for approximating the conditional mean values, when the joint probability distribution is not known, or for calculating the amount of nonlinear dependence between random variables when the joint probability distribution is known. The integral with respect to this signed measure on the sample space is also analyzed.minimizing [chi]2 the closest signed product measure to independence curvature induced by linear dependence between random variables

The curvature induced by covariance

AbstractThe objective of the paper is to construct the signed measure which is the closest one to independence subject to given cavariances between random variables, where closeness is measured by using Pearson's χ2 indicator. The difference between this signed measure and the independent, direct product of the marginals gives the curvature induced by the linear dependence between random variables. The signed measure may be extended to the sample space of a time series and used for approximating the conditional mean values, when the joint probability distribution is not known, or for calculating the amount of nonlinear dependence between random variables when the joint probability distribution is known. The integral with respect to this signed measure on the sample space is also analyzed