Compare and Evaluate the Performance of Gaussian Spatial Regression Models and Skew Gaussian Spatial Regression Based on Kernel Averaged Predictors
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 5, September 2015, Pages: 368-372
Received: Jul. 31, 2015; Accepted: Aug. 10, 2015; Published: Aug. 19, 2015
Views 4100      Downloads 89
Somayeh Shahraki Dehsoukhteh, Department of Statistics, Faculty of Sciences, Zabol University, zabol, Iran
Article Tools
Follow on us
In many problems in the field of spatial statistics, when modeling the trend functions, predictors or covariates are available and the goal is to build a regression model to describe the relationship between the response and predictors. Generally, in spatial regression models, the trend function is often linear and it is assumed that the response mean is a linear function of predictor values in the same location where the response variable is observed. But, in real applications, the neighboring predictors sometimes provide valuable information about the response variable particulary when the distance between the locations is small. Having considered this subject matter, Heaton and Gelfand [6] suggested using kernel averaged predictors for modeling trend functions in which neighboring predictor information are also used. The models proposed by Heaton an Gelfand seemed to be bound by data normality. So, in many more application problems, spatial response variables follow a skew distribution. Therefore, in this article, skew Gaussian spatial regression model is studied and the performance of the model is presented and evaluated in comparison with Gaussian spatial regression models based on kernel averaged predictors using simulation studies and real examples
Spatial Regression, Kernel, Skew Normal
To cite this article
Somayeh Shahraki Dehsoukhteh, Compare and Evaluate the Performance of Gaussian Spatial Regression Models and Skew Gaussian Spatial Regression Based on Kernel Averaged Predictors, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 5, 2015, pp. 368-372. doi: 10.11648/j.ajtas.20150405.17
Arellano-Valle, R. B. and Azzalini, A., “On the Unification of Families of Skew-normal Distributions”, Scandivian Journal of Statistics, 33,561-574, (2006).
Banerjee, S. and Carlin, B. P. and Gelfand, A. E.,” Hierarchical Modeling and Analysis for Spatial Data”, Boca Raton: Chapman and Hall/CRC, (2004).
Chiles, J. P. and Delfiler, P.,” Geostatistics: Modeling Spatial Uncertainty”. New York: Wiley Inter-science, (1999).
Cressie, N., ” Statistics for Spatial Data, Revised edition”, John Wiley, NewYork, (1993).
Cressie, N. and Wikle, C., “statistics for Spatio-Temporal Data”, New York: Wiley, (2011).
Diggle, P. J. and Ribeiro, Jr. P.J,” Model-Based Geostatistics”, Springer Series in Statistics, (2007).
Genton, M. G., “Skew-Symmetric and Generalized Skew-Elliptical Distributions”, In Genton, M. G., Skew-Elliptical Distributions and Their Applications, chapter 5, 81-100, Chapman and Hall/CRC, (2004).
Heaton, M. J. and Gelfand, E.,”Spatial Regression Using Kernel Averaged Predictors”, Journal OfA-gricultural, Biological, and Environmental Statistics, 16:233-252, (2011).
Heaton, M.J.and Gelfand, A.E., “Kernel Averaged Predictors for Spatio-Temporal Regression Models,” Spatial Statistics, 2, 15-32, (2012).
Matern, B., “Spatial Variation”, (2nd,ed), Berlin: Springer, (1986).
Wakernagel, H. “ Multivariate Geostatistics”, Berlin: Springer, (2003).
Zhang, H. and El-Shaarawi, A.,“On Spatial Skew-Gaussian Processes and Applications”, Environ-metrics,21, 33-47, (2010).
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186