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Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process

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  • Zareifard, Hamid
  • Jafari Khaledi, Majid

Abstract

In this paper, we introduce a unified skew Gaussian-log Gaussian model and propose a general class of spatial sampling models that can account for both heavy tails and skewness. This class includes some models proposed previously in the literature. The likelihood function involves analytically intractable integrals and direct maximization of the marginal likelihood is numerically difficult. We obtain maximum likelihood estimates of the model parameters, using a stochastic approximation of the EM algorithm (SAEM). The predictive distribution at unsampled sites is approximated based on Markov chain Monte Carlo samples. The identifiability of the parameters and the performance of the proposed model is investigated by a simulation study. The usefulness of our methodology is demonstrated by analyzing a Pb data set in a region of north Iran.

Suggested Citation

  • Zareifard, Hamid & Jafari Khaledi, Majid, 2013. "Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 16-28.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:16-28
    DOI: 10.1016/j.jmva.2012.07.003
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    References listed on IDEAS

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    8. Lachos, Victor H. & Bandyopadhyay, Dipankar & Garay, Aldo M., 2011. "Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1208-1217, August.
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    Cited by:

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    2. Firoozeh Rivaz & Majid Jafari Khaledi, 2015. "Bayesian spatial prediction of skew and censored data via a hybrid algorithm," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 1993-2009, September.
    3. M. Alodat & M. AL-Rawwash, 2014. "The extended skew Gaussian process for regression," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 317-330, October.
    4. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Reinaldo B. Arellano‐Valle & Víctor Morales‐Oñate, 2021. "Non‐Gaussian geostatistical modeling using (skew) t processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 212-245, March.
    5. Krzysztof Dȩbicki & Enkelejd Hashorva & Lanpeng Ji & Chengxiu Ling, 2015. "Extremes of order statistics of stationary processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 229-248, June.
    6. Masoud Faridi & Majid Jafari Khaledi, 2022. "The polar-generalized normal distribution: properties, Bayesian estimation and applications," Statistical Papers, Springer, vol. 63(2), pages 571-603, April.
    7. Jafari Khaledi, Majid & Zareifard, Hamid & Boojari, Hossein, 2023. "A spatial skew-Gaussian process with a specified covariance function," Statistics & Probability Letters, Elsevier, vol. 192(C).
    8. Kassahun Abere Ayalew & Samuel Manda & Bo Cai, 2021. "A Comparison of Bayesian Spatial Models for HIV Mapping in South Africa," IJERPH, MDPI, vol. 18(21), pages 1-10, October.
    9. Mahmoudian, Behzad, 2018. "On the existence of some skew-Gaussian random field models," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 331-335.
    10. Hossein Boojari & Majid Khaledi & Firoozeh Rivaz, 2016. "A non-homogeneous skew-Gaussian Bayesian spatial model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 55-73, March.

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