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Compare and Evaluate the Performance of Gaussian Spatial Regression Models and Skew Gaussian Spatial Regression Based on Kernel Averaged Predictors

Received: 31 July 2015     Accepted: 10 August 2015     Published: 19 August 2015
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Abstract

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

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 5)
DOI 10.11648/j.ajtas.20150405.17
Page(s) 368-372
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Spatial Regression, Kernel, Skew Normal

References
[1] Arellano-Valle, R. B. and Azzalini, A., “On the Unification of Families of Skew-normal Distributions”, Scandivian Journal of Statistics, 33,561-574, (2006).
[2] Banerjee, S. and Carlin, B. P. and Gelfand, A. E.,” Hierarchical Modeling and Analysis for Spatial Data”, Boca Raton: Chapman and Hall/CRC, (2004).
[3] Chiles, J. P. and Delfiler, P.,” Geostatistics: Modeling Spatial Uncertainty”. New York: Wiley Inter-science, (1999).
[4] Cressie, N., ” Statistics for Spatial Data, Revised edition”, John Wiley, NewYork, (1993).
[5] Cressie, N. and Wikle, C., “statistics for Spatio-Temporal Data”, New York: Wiley, (2011).
[6] Diggle, P. J. and Ribeiro, Jr. P.J,” Model-Based Geostatistics”, Springer Series in Statistics, (2007).
[7] 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).
[8] Heaton, M. J. and Gelfand, E.,”Spatial Regression Using Kernel Averaged Predictors”, Journal OfA-gricultural, Biological, and Environmental Statistics, 16:233-252, (2011).
[9] Heaton, M.J.and Gelfand, A.E., “Kernel Averaged Predictors for Spatio-Temporal Regression Models,” Spatial Statistics, 2, 15-32, (2012).
[10] Matern, B., “Spatial Variation”, (2nd,ed), Berlin: Springer, (1986).
[11] Wakernagel, H. “ Multivariate Geostatistics”, Berlin: Springer, (2003).
[12] Zhang, H. and El-Shaarawi, A.,“On Spatial Skew-Gaussian Processes and Applications”, Environ-metrics,21, 33-47, (2010).
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  • APA Style

    Somayeh Shahraki Dehsoukhteh. (2015). 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, 4(5), 368-372. https://doi.org/10.11648/j.ajtas.20150405.17

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    ACS Style

    Somayeh Shahraki Dehsoukhteh. Compare and Evaluate the Performance of Gaussian Spatial Regression Models and Skew Gaussian Spatial Regression Based on Kernel Averaged Predictors. Am. J. Theor. Appl. Stat. 2015, 4(5), 368-372. doi: 10.11648/j.ajtas.20150405.17

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    AMA Style

    Somayeh Shahraki Dehsoukhteh. Compare and Evaluate the Performance of Gaussian Spatial Regression Models and Skew Gaussian Spatial Regression Based on Kernel Averaged Predictors. Am J Theor Appl Stat. 2015;4(5):368-372. doi: 10.11648/j.ajtas.20150405.17

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  • @article{10.11648/j.ajtas.20150405.17,
      author = {Somayeh Shahraki Dehsoukhteh},
      title = {Compare and Evaluate the Performance of Gaussian Spatial Regression Models and Skew Gaussian Spatial Regression Based on Kernel Averaged Predictors},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {4},
      number = {5},
      pages = {368-372},
      doi = {10.11648/j.ajtas.20150405.17},
      url = {https://doi.org/10.11648/j.ajtas.20150405.17},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150405.17},
      abstract = {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},
     year = {2015}
    }
    

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    AB  - 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
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Author Information
  • Department of Statistics, Faculty of Sciences, Zabol University, zabol, Iran

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