Related papers: Maximum likelihood estimation for Gaussian process…
We study the problem of estimating the covariance parameters of a one-dimensional Gaussian process with exponential covariance function under fixed-domain asymptotics. We show that the weighted pairwise maximum likelihood estimator of the…
We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotic. We first characterize the equivalence of Gaussian measures under this model.…
This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As the Mat\'ern case, this class allows a continuous parameterization of…
The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of…
We consider a one-dimensional Gaussian process having exponential covariance function. Under fixed-domain asymptotics, we prove the strong consistency and asymptotic normality of a cross validation estimator of the microergodic covariance…
We study estimation and prediction of Gaussian processes with covariance model belonging to the generalized Cauchy (GC) family, under fixed domain asymptotics. Gaussian processes with this kind of covariance function provide separate…
This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…
Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…
We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
In parametric estimation of covariance function of Gaussian processes, it is often the case that the true covariance function does not belong to the parametric set used for estimation. This situation is called the misspecified case. In this…
Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…
There has been a growing interest in providing models for multivariate spatial processes. A majority of these models specify a parametric matrix covariance function. Based on observations, the parameters are estimated by maximum likelihood…
The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…
This work considers parameter estimation for Gaussian process interpolation with a periodized version of the Mat{\'e}rn covariance function introduced by Stein. Convergence rates are studied for the joint maximum likelihood estimation of…
We consider a stochastic process model with time trend and measurement error. We establish consistency and derive the limiting distributions of the maximum likelihood (ML) estimators of the covariance function parameters under a general…
Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…
It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Mat\'ern covariance kernel. The smoothness parameter of a Mat\'ern kernel determines many important…