Nonparametric estimation of the variogram and its spectrum

  title={Nonparametric estimation of the variogram and its spectrum},
  author={Chunfeng Huang and Tailen Hsing and Noel Cressie},
In the study of intrinsically stationary spatial processes, a new nonparametric variogram estimator is proposed through its spectral representation. The methodology is based on estimation of the variogram's spectrum by solving a regularized inverse problem through quadratic programming. The estimated variogram is guaranteed to be conditionally negative-definite. Simulation shows that our estimator is flexible and generally has smaller mean integrated squared error than the parametric estimator… 

Figures and Tables from this paper

Semiparametric estimation of spectral density function for irregular spatial data

Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been

Log-periodogram regression of two-dimensional intrinsically stationary random fields

We propose a new semiparametric model for two-dimensional intrinsically stationary random fields and an estimator for the long memory parameter of the model. The model includes a fractional Brownian

Bayesian Nonstationary and Nonparametric Covariance Estimation for Large Spatial Data

Given replicate observations of a Gaussian spatial field, this work proposes nonstationary and nonparametric Bayesian inference on the spatial dependence and proposes a near-linear number of nonzero entries in a sparse Cholesky factor of the precision matrix.

Nonparametric Estimation of Spatial and Space-Time Covariance Function

A nonparametric covariance estimator is proposed for the spatial data, as well as its extension to the spatio-temporal data based on the class of space-time covariance models developed by Gneiting (J. Am. Stat. Assoc. 97:590–600, 2002).

A comparison of sampling grids, cut-off distance and type of residuals in parametric variogram estimation

Simulation experiments show fitting based on the variogram cloud is preferable to that based on Matheron's and Cressie–Hawkins empirical variogram estimators.

Empirical variogram for achieving the best valid variogram

The analysis of the spatial groundwater dataset used in this article suggests that the wave variogram model, with holestted to the empirical VNN variogram is the most appropriate choice to produce the predicted pollution map of the nitrate concentrations in groundwater dataset.


The adaptive parametric nonstationary covariance structure for spatial processes is proposed and the results show that the propose model perform competitively with existing models.

Covariance structure of spatial and spatiotemporal processes

An important aspect of statistical modeling of spatial or spatiotemporal data is to determine the covariance function, a key part of spatial prediction (kriging) and several nonstationary approaches have been developed.

Modeling spatial covariance functions

Choi, InKyung Ph.D., Purdue University, December 2014. Modeling spatial covariance functions. Major Professor: Hao Zhang. Covariance modeling plays a key role in the spatial data analysis as it



Spectral density estimation through a regularized inverse problem

In the study of stationary stochastic processes on the real line, the co- variance function and the spectral density function are parameters of considerable interest. They are equivalent ways of

On the Nonparametric Estimation of Covariance Functions

We describe kernel methods for estimating the covariance function of a stationary stochastic process, and show how to ensure that the estimator has the positive semidefiniteness property. From a

Semiparametric Estimation of Spectral Density With Irregular Observations

This work proposes a semiparametric method for estimating spectral densities of isotropic Gaussian processes with scattered data and compares it with a kernel method proposed by Hall et al. and a parametric method using the Matérn model.

The Variogram and its Estimation

Robustness properties of various variogram estimators are discussed. A closer look at the variogram is made and conditions for the traditional non-parametric estimator to be optimal is presented.

Spectral methods for nonstationary spatial processes

SUMMARY We propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process. We also study the asymptotic properties of the

Isotropic spectral additive models of the covariogram

Summary.  A class of additive covariance models of an isotropic random process is proposed, motivated by the spectral representation of the covariance function. Model parameters are estimated by

Nonparametric Estimation of Nonstationary Spatial Covariance Structure

Abstract Estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks. We introduce a

Geostatistics for natural resources characterization

Variogram.- Improving the Estimation and Modelling of the Variogram.- Towards Resistant Geostatistics.- Statistical Inference of the Semivariogram and the Quadratic Model.- Use of the Jackknife

Smoothing Spline Models with Correlated Random Errors

Abstract Spline-smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model. Their performances depend greatly on the choice of smoothing parameters. Many

Fitting variogram models by weighted least squares

The method of weighted least squares is shown to be an appropriate way of fitting variogram models. The weighting scheme automatically gives most weight to early lags and down-weights those lags with