Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics

DOI10.1214/17-AOS1652zbMath1418.62365arXiv1607.06921OpenAlexW2963502448MaRDI QIDQ1731058

Reinhard Furrer, Moreno Bevilacqua, Emilio Porcu, Tarik Faouzi

Publication date: 6 March 2019

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.06921

zbMATH Keywords

spectral densitylarge datasetcompactly supported covariancemicroergodic parameter

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Inference from stochastic processes and prediction (62M20) Inference from spatial processes (62M30) Prediction theory (aspects of stochastic processes) (60G25)

Related Items (36)

A multi-resolution approximation via linear projection for large spatial datasets ⋮ Necessary and sufficient conditions for asymptotically optimal linear prediction of random fields on compact metric spaces ⋮ Multivariate Gaussian Random Fields over Generalized Product Spaces involving the Hypertorus ⋮ A deep look into the dagum family of isotropic covariance functions ⋮ Spectral conditions for equivalence of Gaussian random fields with stationary increments ⋮ Space-Time Estimation and Prediction under Infill Asymptotics with Compactly Supported Covariance Functions ⋮ Asymptotic properties of the maximum likelihood and cross validation estimators for transformed Gaussian processes ⋮ Extending the Gneiting class for modeling spatially isotropic and temporally symmetric vector random fields ⋮ New validity conditions for the multivariate Matérn coregionalization model, with an application to exploration geochemistry ⋮ A Riemann-Stein kernel method ⋮ Asymptotically equivalent prediction in multivariate geostatistics ⋮ Generalised Wendland functions for the sphere ⋮ Estimating the parameters of some common Gaussian random fields with nugget under fixed-domain asymptotics ⋮ Stein hypothesis and screening effect for covariances with compact support ⋮ Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding ⋮ Assessing the estimation of nearly singular covariance matrices for modeling spatial variables ⋮ Asymptotic analysis of ML-covariance parameter estimators based on covariance approximations ⋮ A flexible Clayton-like spatial copula with application to bounded support data ⋮ Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics ⋮ A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers ⋮ Unifying compactly supported and Matérn covariance functions in spatial statistics ⋮ Modelling Point Referenced Spatial Count Data: A Poisson Process Approach ⋮ Composite likelihood estimation for a Gaussian process under fixed domain asymptotics ⋮ A case study competition among methods for analyzing large spatial data ⋮ Lasso estimation for spherical autoregressive processes ⋮ A Kalman filter method for estimation and prediction of space-time data with an autoregressive structure ⋮ On the inference of applying Gaussian process modeling to a deterministic function ⋮ Maximum likelihood estimation for Gaussian processes under inequality constraints ⋮ Estimation and prediction of Gaussian processes using generalized Cauchy covariance model under fixed domain asymptotics ⋮ Unnamed Item ⋮ The SPDE approach to Matérn fields: graph representations ⋮ Discussion on competition for spatial statistics for large datasets ⋮ On information about covariance parameters in Gaussian Matérn random fields ⋮ Asymptotic Analysis of Maximum Likelihood Estimation of Covariance Parameters for Gaussian Processes: An Introduction with Proofs ⋮ Bayesian fixed-domain asymptotics for covariance parameters in a Gaussian process model ⋮ On positive definiteness of some radial functions

Uses Software

• spam
• George

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic properties of multivariate tapering for estimation and prediction
• Covariance tapering for prediction of large spatial data sets in transformed random fields
• Wendland functions with increasing smoothness converge to a Gaussian
• The missing Wendland functions
• A simple condition for asymptotic optimality of linear predictions of random fields
• Uniform asymptotic optimality of linear predictions of a random field using an incorrect second-order structure
• Fixed-domain asymptotic properties of tapered maximum likelihood estimators
• Asymptotically efficient prediction of a random field with a missspecified covariance function
• On Abel-Poisson type and Riesz means
• Correlation theory of stationary and related random functions. Volume I: Basic results
• Interpolation of spatial data. Some theory for kriging
• Predicting random fields with increasing dense observations
• Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics
• Compactly supported correlation functions
• Equivalence of Gaussian measures for some nonstationary random fields
• Compactly supported positive definite radial functions
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• On fixed-domain asymptotics and covariance tapering in Gaussian random field models
• Closed form representations and properties of the generalised Wendland functions
• On the consistent separation of scale and variance for Gaussian random fields
• Grünbaum's inequality for Bessel functions
• Maximum likelihood estimation of models for residual covariance in spatial regression
• On some properties of Buhmann functions
• Towards reconciling two asymptotic frameworks in spatial statistics
• Nonseparable, Stationary Covariance Functions for Space–Time Data
• On Absolute Continuity of Measures Corresponding to Homogeneous Gaussian Fields
• The role of the range parameter for estimation and prediction in geostatistics
• Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets
• Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics
• On the effect of covariance function estimation on the accuracy of kriging predictors

This page was built for publication: Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics