Related papers: Multivariate Mat\'ern Models -- A Spectral Approac…
The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the…
In this work we present full Bayesian inference for a new flexible nonseparable class of cross-covariance functions for multivariate spatial data. A Bayesian test is proposed for separability of covariance functions which is much more…
The Mat\'ern family of covariance functions is currently the most popularly used model in spatial statistics, geostatistics, and machine learning to specify the correlation between two geographical locations based on spatial distance.…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…
Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…
The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
Uncertainty is an inherent characteristic of biological and geospatial data which is almost made by measurement error in the observed values of the quantity of interest. Ignoring measurement error can lead to biased estimates and inflated…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…
Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed…
Covariance functions are the core of spatial statistics, stochastic processes, machine learning as well as many other theoretical and applied disciplines. The properties of the covariance function at small and large distances determine the…
This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of new solution…
Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…
The Mat\'ern covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Mat\'ern class is that it is possible to get precise control over the degree of…
This paper deals with M$^2$-signals, namely multivariate (or vector-valued) signals defined over a multidimensional domain. In particular, we propose an optimization technique to solve the covariance extension problem for stationary random…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…