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Variogram estimation in the presence of trend
Nikolay Bliznyuk1, Raymond J Carroll, Marc G Genton
1Department of Statistics, University of Florida, 406 McCarty C, Gainesville, Florida 32611-0339, USA.
Statistics and Its Interface
|June 28, 2012
Summary
This study introduces a new method for estimating covariance function parameters in spatial statistics, correcting for unknown smooth trends. This improves nonparametric trend estimation and variogram parameter accuracy.
Area of Science:
- Spatial statistics
- Geostatistics
- Statistical modeling
Background:
- Estimating covariance function parameters is crucial for accurate nonparametric trend estimation.
- Existing methods often ignore smooth trends, leading to biased variogram parameter estimates.
- This bias hinders reliable analysis in spatial data.
Purpose of the Study:
- To develop a novel estimator for covariance function parameters that accounts for unknown smooth trends.
- To correct for bias introduced by trend effects in variogram parameter estimation.
- To provide a more robust method for spatial data analysis.
Main Methods:
- Regressing squared differences of the response on their expectations.
- Incorporating an offset term to account for the trend's influence on the variogram.
- Asymptotic justification under the increasing domain framework.
Main Results:
- The proposed estimator corrects for bias caused by ignoring smooth trends.
- Simulation studies show favorable comparisons with existing estimators.
- The method makes less restrictive assumptions than current approaches.
Conclusions:
- The developed method offers improved accuracy in estimating variogram parameters.
- This technique enhances nonparametric trend estimation in the presence of spatial dependence.
- The approach is applicable to various contexts beyond spatial statistics, including U.S. precipitation data analysis.
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