Related papers: Derivation of Correlation Dimension from Spatial A…
This article introduces autocorrelograms for time series of point processes. Such time series usually arise when a longer temporal or spatio-temporal point process is sliced into smaller time units; for example, when an annual process is…
Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, Szekely et. al. (2007). We propose an objective which is free of…
In this paper, we address the problem of predicting a response variable in the context of both, spatially correlated and high-dimensional data. To reduce the dimensionality of the predictor variables, we apply the sufficient dimension…
We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent…
The effective sample size quantifies the amount of independent information contained in a dataset, accounting for redundancy due to correlation between observations. While widely used in geostatistics for scalar data, its extension to…
Detecting dependence between variables is a crucial issue in statistical science. In this paper, we propose a novel metric called label projection correlation to measure the dependence between numerical and categorical variables. The…
Detecting spatial patterns is fundamental to scientific discovery, yet current methods lack statistical consensus and face computational barriers when applied to large-scale spatial omics datasets. We unify major approaches through a single…
Dynamical phenomena such as infectious diseases are often investigated by following up subjects longitudinally, thus generating time to event data. The spatial aspect of such data is also of primordial importance, as many infectious…
The correlation dimension of natural language is measured by applying the Grassberger-Procaccia algorithm to high-dimensional sequences produced by a large-scale language model. This method, previously studied only in a Euclidean space, is…
When observing spatial data, what standard errors should we report? With the finite population framework, we identify three channels of spatial correlation: sampling scheme, assignment design, and model specification. The Eicker-Huber-White…
Building upon the Chatterjee correlation (2021: J. Am. Stat. Assoc. 116, p2009) for two real-valued variables, this study introduces a generalized measure of directed association between two vector variables, real or complex-valued, and of…
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…
Eigenmaps are important in analysis, geometry, and machine learning, especially in nonlinear dimension reduction. Approximation of the eigenmaps of a Laplace operator depends crucially on the scaling parameter $\epsilon$. If $\epsilon$ is…
Many ecological and spatial processes are complex in nature and are not accurately modeled by linear models. Regression trees promise to handle the high-order interactions that are present in ecological and spatial datasets, but fail to…
Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…
The correlation dimension, that is, the dimension obtained by computing the correlation function of pairs of points of a trajectory in phase space, is a numerical technique introduced in the field of nonlinear dynamics in order to compute…
Accurate estimation for extent of cross{sectional dependence in large panel data analysis is paramount to further statistical analysis on the data under study. Grouping more data with weak relations (cross{sectional dependence) together…
The autologistic model and related auto-models, commonly applied as autocovariate regression, offer distinct advantages for analysing spatially autocorrelated ecological data. However, comparative studies by Carl and K\"uhn (Ecol. Model.,…