Related papers: The spatial sign covariance matrix and its applica…
Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to…
Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to…
Due to the increasing recording capability, functional data analysis has become an important research topic. For functional data the study of outlier detection and/or the development of robust statistical procedures has started recently.…
We discuss the combining of measurements where single measurement covariances are given but the joint measurement covariance is unknown. For this paper we assume the mapping of a single measurement to the solution space is the identity…
We propose a fast bivariate smoothing approach for symmetric surfaces that has a wide range of applications. We show how it can be applied to estimate the covariance function in longitudinal data as well as multiple additive covariances in…
We describe a statistical model to estimate the covariance matrix of matter tracer two-point correlation functions with cosmological simulations. Assuming a fixed number of cosmological simulation runs, we describe how to build a…
Many multivariate statistical methods rely heavily on the sample covariance matrix. It is well known though that the sample covariance matrix is highly non-robust. One popular alternative approach for "robustifying" the multivariate method…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
This paper investigates the spectral properties of spatial-sign covariance matrices, a self-normalized version of sample covariance matrices, for data from $\alpha$-regularly varying populations with general covariance structures. By…
We derive in this paper expressions for the covariance matrix of the cosmic shear two-point correlation functions which are readily applied to any survey geometry. Furthermore, we consider the more special case of a simple survey geometry…
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
When modeling geostatistical or areal data, spatial structure is commonly accommodated via a covariance function for the former and a neighborhood structure for the latter. In both cases the resulting spatial structure is a consequence of…
The idea of spatial crosscorrelation was conceived of long ago. However, unlike the related spatial autocorrelation, the theory and method of spatial crosscorrelation analysis have remained undeveloped. This paper presents a set of models…
Spatial association measures for univariate static spatial data are widely used. When the data is in the form of a collection of spatial vectors with the same temporal domain of interest, we construct a measure of similarity between the…
Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…
It is critical to understand the properties of spatial correlation matrices in massive multiple-input multiple-output (MIMO) systems. We derive new bounds on the extreme eigenvalues of a spatial correlation matrix that is characterized by…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
Based on standardized vector and globally normalized weight matrix, Moran's index of spatial autocorrelation analysis has been expressed as a formula of quadratic form. Further, based on this formula, an inner product equation and outer…