We specify a class of Gaussian rank-r latent models for cross-covariance. We show by construction that any variance-covariance matrix for the observed variables induced by rank-r reduced-rank regression can be induced by a rank-r latent model. 1 Model specification Basic terms are introduced which will be used to state the result. 1.1 Rank-r constraint models Let p be the number of X-variables ...

The paper obtains the general form of the cross-covariance function of vector fractional Brownian motion with correlated components having different self-similarity indices.

Abstract: In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance structure. As an application, we provide an asymptotic power function for the corrected likelihood ratio statistic for testing the presence of spi...

We investigated the meridional circulation of photospheric faculae throughout cycle 19. Together with the rotation observed in a companion paper (Meunier et al. 1996), we were able to address the problem of the existence of the observed differential rotation. Themeridional circulation is characterized by a strong north-south asymmetry. The distribution of meridional circulation around the mean ...

We describe a method for causal inference that measures the strength of statistical dependence by the Hilbert-Schmidt norm of kernelbased conditional cross-covariance operators. We consider the increase of the dependence of two variables X and Y by conditioning on a third variable Z as a hint for Z being a common effect of X and Y . Based on this assumption, we collect “votes” for hypothetical ...

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.

Many spatial processes in environmental applications, such as climate variables and climate model errors on a global scale, exhibit complex nonstationary dependence structure, in not only their marginal covariance but also their cross-covariance. Flexible crosscovariance models for processes on a global scale are critical for an accurate description of each spatial process as well as the cross-...