Least squares variogram fitting by spatial subsampling
Address for correspondence
: Soumendra N. Lahiri, Department of Statistics, Iowa State University, Ames, IA 50011‐1210, USA.
E‐mail: snlahiri@iastate.edu
Abstract
Summary. Least squares methods are popular for fitting valid variogram models to spatial data. The paper proposes a new least squares method based on spatial subsampling for variogram model fitting. We show that the method proposed is statistically efficient among a class of least squares methods, including the generalized least squares method. Further, it is computationally much simpler than the generalized least squares method. The method produces valid variogram estimators under very mild regularity conditions on the underlying random field and may be applied with different choices of the generic variogram estimator without analytical calculation. An extension of the method proposed to a class of spatial regression models is illustrated with a real data example. Results from a simulation study on finite sample properties of the method are also reported.
Citing Literature
Number of times cited according to CrossRef: 15
- Mohd Zaharifudin Muhamad Ali, Faridah Othman, Raingauge network optimization in a tropical urban area by coupling cross-validation with the geostatistical technique, Hydrological Sciences Journal, 10.1080/02626667.2018.1437271, 63, 3, (474-491), (2018).
- Moreno Bevilacqua, Alfredo Alegria, Daira Velandia, Emilio Porcu, Composite Likelihood Inference for Multivariate Gaussian Random Fields, Journal of Agricultural, Biological, and Environmental Statistics, 10.1007/s13253-016-0256-3, 21, 3, (448-469), (2016).
- Naima Mubarak, Ijaz Hussain, Muhammad Faisal, Tajammal Hussain, Muhammad Yousaf Shad, Nasser M. AbdEl-Salam, Javid Shabbir, Spatial Distribution of Sulfate Concentration in Groundwater of South-Punjab, Pakistan, Water Quality, Exposure and Health, 10.1007/s12403-015-0165-7, 7, 4, (503-513), (2015).
- Moreno Bevilacqua, Federico Crudu, Emilio Porcu, Combining Euclidean and composite likelihood for binary spatial data estimation, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-014-0938-8, 29, 2, (335-346), (2014).
- Moreno Bevilacqua, Carlo Gaetan, Comparing composite likelihood methods based on pairs for spatial Gaussian random fields, Statistics and Computing, 10.1007/s11222-014-9460-6, 25, 5, (877-892), (2014).
- Youngsoo Choi, Yoon-Dong Lee, Improved Generalized Method of Moment Estimators to Estimate Diffusion Models, Korean Journal of Applied Statistics, 10.5351/KJAS.2013.26.5.767, 26, 5, (767-783), (2013).
- Moreno Bevilacqua, Carlo Gaetan, Jorge Mateu, Emilio Porcu, Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach, Journal of the American Statistical Association, 10.1080/01621459.2011.646928, 107, 497, (268-280), (2012).
- Yun Bai, Peter X.‐K. Song, T. E. Raghunathan, Joint composite estimating functions in spatiotemporal models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 10.1111/j.1467-9868.2012.01035.x, 74, 5, (799-824), (2012).
- Kedar Patel, Soumendra N. Lahiri, Costas J. Spanos, Robust estimation of line width roughness parameters, Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena, 10.1116/1.3517718, 28, 6, (C6H18-C6H33), (2010).
- C. Ma, Intrinsically Stationary Variograms in Space and Time, Theory of Probability & Its Applications, 10.1137/S0040585X97983481, 53, 1, (145-155), (2009).
- Chunsheng Ma, Chunsheng Ma, Intrinsically Stationary Variograms in Space and TimeIntrinsically Stationary Variograms in Space and Time, Теория вероятностей и ее примененияTeoriya Veroyatnostei i ee Primeneniya, 10.4213/tvp2494, 53, 1, (189-200), (2008).
- Daniel J. Nordman, An empirical likelihood method for spatial regression, Metrika, 10.1007/s00184-007-0167-y, 68, 3, (351-363), (2008).
- Cavan Reilly, Andrew Gelman, Weighted Classical Variogram Estimation for Data With Clustering, Technometrics, 10.1198/004017006000000282, 49, 2, (184-194), (2007).
- Yongtao Guan, Michael Sherman, On least squares fitting for stationary spatial point processes, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 10.1111/j.1467-9868.2007.00575.x, 69, 1, (31-49), (2007).
- Hye-Mi Choi, One-step Least Squares Fitting of Variogram, Communications for Statistical Applications and Methods, 10.5351/CKSS.2005.12.2.539, 12, 2, (539-544), (2005).
