Related papers: Derivation of Correlation Dimension from Spatial A…
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…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor…
While spatially varying coefficient (SVC) modeling is popular in applied science, its computational burden is substantial. This is especially true if a multiscale property of SVC is considered. Given this background, this study develops a…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
Standard cosmology is based on the assumption that the universe is spatially homogeneous. However the consensus on a homogeneous matter structure, even on very large scales, has never been complete. The advantage of correlation dimension…
Spatial scan statistics are well-known methods for cluster detection and are widely used in epidemiology and medical studies for detecting and evaluating the statistical significance of disease hotspots. For the sake of simplicity, the…
Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves $X(\mathbf{s}_k;t),t\in[0,T],$ observed at spatial locations…
We investigate the short-time dynamic relaxation of the two-dimensional XY model in the high temperature phase. Starting from the ordered state, we measure the autocorrelation function and determine the autocorrelation time. It is shown…
This study demonstrates how to use the "spmoran" package implementing scalable spatial regression models for Gaussian and non-Gaussian data. Implemented models include spatially varying coefficient models, models with group effects, spatial…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Dominant features of spatial data are connected structures or patterns that emerge from location-based variation and manifest at specific scales or resolutions. To identify dominant features, we propose a sequential application of…
We summarize properties of the spatial sign covariance matrix and especially look at the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…
This is a "spatial autocorrelation analysis" of spatial autocorrelation. I use the 1-dimension spatial autocorrelation function (ACF) and partial autocorrelation function (PACF) to analyze four kinds of weight function in common use for the…
The hypothesis of self-organized criticality explains the existence of long-range `space-time' correlations, observed inseparably in many natural dynamical systems. A simple link between these correlations is yet unclear, particularly in…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…