Related papers: The spatial sign covariance matrix and its applica…
This paper offers an expository overview of the field of spatial econometrics. It first justifies the necessity of special statistical procedures for the analysis of spatial data and then proceeds to describe the fundamentals of these…
We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the…
Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…
In this article, we define the matricization of a tensor and we present some properties of the matricization. After that, we define the determinant of a tensor and we present some properties of the determinant. We define the covariance…
Image based diagnostics are interpreted in the context of spatial resolution. The same is true for tomographic image reconstruction. Current empirically driven approaches to quantify spatial resolution rely on a deterministic formulation…
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…
In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
The joint estimation of the location vector and the shape matrix of a set of independent and identically Complex Elliptically Symmetric (CES) distributed observations is investigated from both the theoretical and computational viewpoints.…
In this paper we explore a covariance spectral modelling strategy for spatial-temporal processes which involves a spectral approach for time but a covariance approach for space.It facilitates the analysis of coherence between the temporal…
We introduce a novel class of non-stationary covariance functions for random fields on linear networks that allows both the variance and the correlation range of the random field to vary spatially. The proposed covariance functions are…
Using 1000 ray-tracing simulations for a {\Lambda}-dominated cold dark model in Sato et al. (2009), we study the covariance matrix of cosmic shear correlation functions, which is the standard statistics used in the previous measurements.…
The problem of estimating the covariance matrix $\Sigma$ of a $p$-variate distribution based on its $n$ observations arises in many data analysis contexts. While for $n>p$, the classical sample covariance matrix $\hat{\Sigma}_n$ is a good…
As the spatial features of multivariate data are increasingly central in researchers' applied problems, there is a growing demand for novel spatially-aware methods that are flexible, easily interpretable, and scalable to large data. We…
In order to pursue the issue of the relation between the financial cross-correlations and the conventional Random Matrix Theory we analyse several characteristics of the stock market correlation matrices like the distribution of…
The relation between Pearson's correlation coefficient and Salton's cosine measure is revealed based on the different possible values of the division of the L1-norm and the L2-norm of a vector. These different values yield a sheaf of…
We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix…
The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…
Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong.…
This paper develops a novel spatial quantile function-on-scalar regression model, which studies the conditional spatial distribution of a high-dimensional functional response given scalar predictors. With the strength of both quantile…