# Nonparametric estimation of the variogram and its spectrum

@article{Huang2011NonparametricEO, title={Nonparametric estimation of the variogram and its spectrum}, author={Chunfeng Huang and Tailen Hsing and Noel Cressie}, journal={Biometrika}, year={2011}, volume={98}, pages={775-789} }

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…

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## References

SHOWING 1-10 OF 45 REFERENCES

### Spectral density estimation through a regularized inverse problem

- Mathematics
- 2011

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

- Mathematics
- 1994

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

- Computer Science, Mathematics
- 2007

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

- Mathematics
- 1984

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

- Mathematics
- 2002

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

- Mathematics
- 2008

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

- Mathematics
- 1992

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

- Geology
- 1984

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

- Mathematics
- 1998

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

- Mathematics
- 1985

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…