Related papers: Radial Covariance Functions Motivated by Spatial R…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if…
Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem (Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely represented as the…
Ratios of integrals can be bounded in terms of ratios of integrands under certain monotonicity conditions. This result, related with L'H\^{o}pital's monotone rule, can be used to obtain sharp bounds for cumulative distribution functions. We…
Series expansions of isotropic Gaussian random fields on $\mathbb{S}^2$ with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localised structure provide an alternative to…
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
In this paper, we characterize several classes of continuous radial basis functions that can be employed to determine whether a interaction of a probability is zero or not. These functions encompass standard independence tests but also the…
In this paper, we provide explicit formulas, in terms of the covariances of sample covariances or sample correlations, for the asymptotic covariances of unrotated factor loading estimates and unique variance estimates. These estimates are…
Stochastic symmetries and related invariance properties of finite dimensional SDEs driven by general c\`adl\`ag semimartingales taking values in Lie groups are defined and investigated. In order to enlarge the class of possible symmetries…
We study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows one of the Ewens measures on the symmetric group. If we apply a smooth enough…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
A crucial assumption to reduce computational complexity in spatial-temporal data analysis is separability, which factors the covariance structure into a purely spatial and a purely temporal component. In this paper, we develop statistical…
Spatial confounding is a fundamental issue in spatial regression models which arises because spatial random effects, included to approximate unmeasured spatial variation, are typically not independent of covariates in the model. This can…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
To investigate and specify the statistical properties of cosmological fields with particular attention to possible non-Gaussian features, accurate formulae for the bispectrum and the bispectrum covariance are required. The bispectrum is the…
Let $(A_x)_{x\in\mathbb{R}^d}$ be a locally integrable, centered, weakly stationary random field, i.e. $\mathbb{E}[A_x]=0$, ${\rm Cov}(A_x,A_y)=K(x-y)$, $\forall x,y\in\mathbb{R}^d$, with measurable covariance function…
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…
Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the…
Rank-based dependence measures such as Spearman's footrule are robust and invariant, but they often fail to capture directional or asymmetric dependence in multivariate settings. This paper introduces a new family of directional Spearman's…
Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for…