相关论文: Hybrid Parametric Classes of Isotropic Covariance …

I consider the Lerch-Hurwitz or periodic zeta function as covariance function of a periodic continuous-time stationary stochastic process. The function can be parametrized with a continuous index $\nu$ which regulates the continuity and…

This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural…

Some of the most outstanding questions in the field of gravitation and geometry remain unsolved as a result of our limited understanding of the global structure of the spacetime geometry and the role played by global spacetime…

Coarse geometry is the study of large-scale properties of spaces. In this paper we study group coarse structures (i.e., coarse structures on groups that agree with the algebraic structures), by using group ideals. We introduce a large class…

This article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic…

In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in…

This article explores the optimization of variational approximations for posterior covariances of Gaussian multiway arrays. To achieve this, we establish a natural differential geometric optimization framework on the space using the…

Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…

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…

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…

Air pollution is a great concern because of its impact on human health and on the environment. Statistical models play an important role in improving knowledge of this complex spatio-temporal phenomenon and in supporting public agencies and…

This work reveals a fundamental link between general covariance and Birkhoff's theorem. We extend Birkhoff's theorem from general relativity to a broad class of generally covariant gravity theories formulated in the Hamiltonian framework.…

This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…

Understanding covariate-varying interdependencies among features is of great interest in various applications. Motivated by microbiome studies where microbial abundances and interactions vary with environmental factors, we develop a…

With the covariant formulation in hand from the first paper of this series (physics/9801019), we begin in this second paper to study the canonical (or ``instantaneous'') formulation of classical field theories. The canonical formluation…

Classical isomorphism theorems due to Dynkin, Eisenbaum, Le Jan, and Sznitman establish equalities between the correlation functions or distributions of occupation times of random paths or ensembles of paths and Markovian fields, such as…

Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…

With the emergence of deep learning, metric learning has gained significant popularity in numerous machine learning tasks dealing with complex and large-scale datasets, such as information retrieval, object recognition and recommendation…

The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…