Detecting independence of random vectors: generalized distance covariance and Gaussian covariance

Gaussian Fields and Gaussian Sheets with Generalized Cauchy Covariance Structure

Abstract. Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transf...

Autoregressive Gaussian Random Vectors of First Order

Deep Gaussian Covariance Network

The correlation length-scale θ next to the noise variance σ are the most used hyperparameters for the Gaussian processes GP . Typically stationary covariance functions k(xi,xj) are used, which are only dependent on the distances between input points τ = ||xi − xj || and thus invariant to the translations in the input space X . The optimization of the hyperparameters is commonly done by maximizi...

Sample Covariance Matrix for Random Vectors with Heavy Tails

1 This research was supported by a research scholarship for the Volkswagen St i f tung Research in Pairs program at Oberwolfach, Germany. 2 Department of Mathematics, University of Nevada. Reno, Nevada 89557. E-mail: mcubed(a unr.edu. 3 Department of Mathematics, University of Dortmund, 44221 Dortmund Germany. E-mail: hps(a mathematik.uni-dortmund.de. We compute the asymptotic distribution of t...

Brownian distance covariance

Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero i...