相关论文: Optimal Scale Invariant Wigner Spectrum Estimation…

We study locally self-similar processes (LSSPs) in Silverman's sense. By deriving the minimum mean-square optimal kernel within Cohen's class counterpart of time-frequency representations, we obtain an optimal estimation for the scale…

We propose a novel error analysis framework for scaled generalized Laguerre and generalized Hermite approximations.This framework can be regarded as an analogue of the Nyquist-Shannon sampling theorem: It characterizes the spatial and…

We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage. Our approach can be interpreted either as estimating the global power spectrum of a stationary process when…

We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…

Hermite polynomials and functions have extensive applications in scientific and engineering problems. Although it is recognized that employing the scaled Hermite functions rather than the standard ones can remarkably enhance the…

In this paper we reconsider the notion of an optimal effective Hamiltonian for the semiclassical propagation of the Wigner distribution in phase space. An explicit expression for the optimal effective Hamiltonian is obtained in the short…

We obtain estimates for the Mean Squared Error (MSE) for the multitaper spectral estimator and certain compressive acquisition methods for multi-band signals. We confirm a fact discovered by Thomson [Spectrum estimation and harmonic…

The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…

This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…

We present a theoretical method for calculating optical absorption spectra based on maximally localized Wannier functions, which is suitable for large periodic systems. For this purpose, we calculate the exciton Hamiltonian, which…

We consider the estimation of the covariance of a stationary Gaussian process on a multi-dimensional grid from observations taken on a general acquisition domain. We derive spectral-norm risk rates for multi-taper estimators. When applied…

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…

Gaussian processes are a powerful class of non-linear models, but have limited applicability for larger datasets due to their high computational complexity. In such cases, approximate methods are required, for example, the recently…

The relative root mean squared errors (RMSE) of nonparametric methods for spectral estimation is compared for microwave scattering data of plasma fluctuations. These methods reduce the variance of the periodogram estimate by averaging the…

Gaussian processes are widely used for accurate emulation of unknown surfaces in sequential design of expensive simulation experiments. Integrated mean squared error (IMSE) is an effective acquisition function for sequential designs based…

We propose a Hermite spectral method for the spatially inhomogeneous Boltzmann equation. For the inverse-power-law model, we generalize an approximate quadratic collision operator defined in the normalized and dimensionless setting to an…

This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing…

We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…

In this paper, an approximation of the optimal compressor function using the quadratic spline functions has been presented. The coefficients of the quadratic spline functions are determined by minimizing the mean-square error (MSE). Based…