Related papers: Asymptotic Spectral Theory for Spatial Data
This article develops a unified framework to study the asymptotic properties of all periodic spline-based estimators, that is, of regression, penalized and smoothing splines. The explicit form of the periodic Demmler-Reinsch basis in terms…
We consider a statistical model of a n-mode quantum Gaussian state which is shift invariant and also gauge invariant. Such models can be considered analogs of classical Gaussian stationary time series, parametrized by their spectral…
Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…
We obtain spectral asymptotics for the quantized derivatives of elements from the first-order homogeneous Sobolev space on the quantum Euclidean space, extending an earlier result of McDonald, Sukochev and Xiong (Commun. Math. Phys. 2020).…
In this paper, we develop spectral and post-spectral estimators for grouped panel data models. Both estimators are consistent in the asymptotics where the number of observations $N$ and the number of time periods $T$ simultaneously grow…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…
The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…
Given a semiring with a preorder subject to certain conditions, the asymptotic spectrum, as introduced by Strassen (J. reine angew. Math. 1988), is a compact Hausdorff space together with a map from the semiring to the ring of continuous…
In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…
In this paper we investigate the asymptotic behavior of the cosmological model based on phantom scalar field on the ground of qualitative analysis of the system of the cosmological model's differential equations and show that as opposed to…
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 study properties of spectral minimal partitions of metric graphs within the framework recently introduced in [Kennedy et al, Calc. Var. 60 (2021), 61]. We provide sharp lower and upper estimates for minimal partition energies in…
We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both…
We introduce a nonparametric spectral density estimator for continuous-time and continuous-space processes measured at fully irregular locations. Our estimator is constructed using a weighted nonuniform Fourier sum whose weights yield a…
A statistic can be a function of multiple samples. There is little existing work on asymptotic theory for such statistics when group membership is random. We propose a flexible framework that can handle both deterministic and random…
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…
This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…
For a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain, this paper derives a general form of its covariance matrix function and provides a series representation for the random…
The self-adjoint matrix Sturm-Liouville operator on a finite interval with a boundary condition in the general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered operator. These…