Document Type : Original Paper

Authors

1 1 Department of Statistics, Higher Education Center of Eghlid, Eghlid, Islamic Republic of Iran

2 2 Department of Statistics, Faculty of Sciences, Shiraz University, Shiraz, Islamic Republic of Iran

3 3 Department of Statistics, Faculty of Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran

Abstract

In this paper, we define a spatial skew and heavy-tailed random field by an extended version of multivariate generalized skew Laplace distribution. The Bayesian spatial regression model is developed to explain the spatial data. A simulation study is then carried out to validate and evaluate the performance of the proposed model. The application of this model is also demonstrated in an analysis of a geological real data set.

Keywords

  1. Anselin L. Spatial Econometrics, methods and models (Kluwer, Dordrecht) 1988.
  2. Anselin L. Spatial dependence and spatial structural instability in applied regression analysis. J Region Sci. 1990; 30: 185-207.
  3. Bustos O, Ojeda S and Vallejos R. Spatial ARMA models and its applications to image filtering. Brazil J Probab Stat. 2009; (23) 2: 141–165.
  4. Shin DW and Sarkar S. Parameter estimation in regression models with auto-correlated errors using irregular data. Commun Stat Theory Methods. 1994; 23: 3567-3580.
  5. Dogan O. Heteroskedasticity of unknown form in spatial autoregressive models with a moving average disturbance term. Econometrics. 2015; 3: 101-127.
  6. Oh M, Shin DW and Kim HJ. Bayesian analysis of regression models with spatially correlated errors and missing observations. Comput Stat Data Analys. 2002; 39: 387-400.
  7. Basu S and Reinsel GC. Regression models with spatially correlated errors. J Am Stat Assoc. 1994; 89: 88-99.
  8. Kim H-M and Mallick BA. Bayesian prediction using the skew Gaussian distribution. J Stat Plan Infer. 2004; 120: 85-101.
  9.  

 

  • Karimi O and Mohammadzadeh M. Bayesian spatial regression models with CSN correlated errors and missing observations. Stat Papers. 2012; 53: 205-218.
  • Saber MM, Nematollahi AR and Mohammadzadeh M. Generalized asymmetric Laplace random fields: existence and application. J Data Sci. 2018; 18: 51-68.
  • Kozubowski TJ, Podgórski K and Rychlik I. Multivariate generalized Laplace distribution and related random fields. J Multivar Analys. 2013; 113: 59–72.
  • Saber MM, Nematollahi AR and Mohammadzadeh M. Generalized Skew Laplace Random Fields: Bayesian Spatial Prediction for Skew and Heavy Tailed Data. J Stat Theory Appl, In Press.
  • Farzammehr MA, Zadkarami MR, McLachlan GJ and Lee SX. Skew-normal Bayesian spatial heterogeneity panel data models. J Appl Stat. 2020; 47(5): 804-826.
  • Kotz S, Kozubowski TJ and Podgórski K. The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering and Finance, Birkhäuser, Boston 2001.