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Multi-dimensional multivariate Gaussian Markov random fields with application to image processing

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  • Mardia, K. V.

Abstract

Recently, numerous practical applications of multivariate Gaussian Markov random fields (GMRF) on a lattice have emerged. However, the theory is not satisfactorily developed. We give various properties of multivariate GMRF for multi-dimensional lattice. In particular, some multivariate MRF are given. We discuss estimation procedures and give a numerical example from the area of image processing.

Suggested Citation

  • Mardia, K. V., 1988. "Multi-dimensional multivariate Gaussian Markov random fields with application to image processing," Journal of Multivariate Analysis, Elsevier, vol. 24(2), pages 265-284, February.
  • Handle: RePEc:eee:jmvana:v:24:y:1988:i:2:p:265-284
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    References listed on IDEAS

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    1. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    2. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    3. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
    4. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
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    Cited by:

    1. Gamerman, Dani & Moreira, Ajax R. B. & Rue, Havard, 2003. "Space-varying regression models: specifications and simulation," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 513-533, March.
    2. Peter Congdon, 2014. "Estimating life expectancies for US small areas: a regression framework," Journal of Geographical Systems, Springer, vol. 16(1), pages 1-18, January.
    3. Amir Kavousi & Mohammad Meshkani & Mohsen Mohammadzadeh, 2011. "Spatial analysis of auto-multivariate lattice data," Statistical Papers, Springer, vol. 52(4), pages 937-952, November.
    4. Dani Gamerman & Ajax R. B. Moreira, 2015. "Multivariate Spatial Regression Models," Discussion Papers 0116, Instituto de Pesquisa Econômica Aplicada - IPEA.
    5. Song, J.J. & Ghosh, M. & Miaou, S. & Mallick, B., 2006. "Bayesian multivariate spatial models for roadway traffic crash mapping," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 246-273, January.
    6. Arnab Bhattacharjee & Eduardo Castro & Taps Maiti & João Marques, 2014. "Endogenous spatial structure and delineation of submarkets: A new framework with application to housing markets," SEEC Discussion Papers 1403, Spatial Economics and Econometrics Centre, Heriot Watt University.
    7. Sain, Stephan R. & Cressie, Noel, 2007. "A spatial model for multivariate lattice data," Journal of Econometrics, Elsevier, vol. 140(1), pages 226-259, September.
    8. Nishii, Ryuei & Eguchi, Shinto, 2006. "Image classification based on Markov random field models with Jeffreys divergence," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1997-2008, October.
    9. Wheeler, David C. & Hickson, DeMarc A. & Waller, Lance A., 2010. "Assessing local model adequacy in Bayesian hierarchical models using the partitioned deviance information criterion," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1657-1671, June.
    10. Xiaoping Jin & Sudipto Banerjee & Bradley P. Carlin, 2007. "Order-free co-regionalized areal data models with application to multiple-disease mapping," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 817-838.
    11. repec:bla:jorssa:v:180:y:2017:i:1:p:119-139 is not listed on IDEAS
    12. Gamerman, Dani & Moreira, Ajax R. B., 2004. "Multivariate spatial regression models," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 262-281, November.

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