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Estimating spatial covariance using penalised likelihood with weighted penalty

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  • Zhengyuan Zhu
  • Yufeng Liu

Abstract

In spatial statistics, the estimation of covariance matrices is of great importance because of its role in spatial prediction and design. In this paper, we propose a penalised likelihood approach with weighted L1 regularisation to estimate the covariance matrix for spatial Gaussian Markov random field models with unspecified neighbourhood structures. A new algorithm for ordering spatial points is proposed such that the corresponding precision matrix can be estimated more effectively. Furthermore, we develop an efficient algorithm to minimise the penalised likelihood via a novel usage of the regularised solution path algorithm, which does not require the use of iterative algorithms. By exploiting the sparsity structure in the precision matrix, we show that the LASSO type of approach gives improved covariance estimators measured by several criteria. Asymptotic properties of our proposed estimator are derived. Both our simulated examples and an application to the rainfall data set show that the proposed method performs competitively.

Suggested Citation

  • Zhengyuan Zhu & Yufeng Liu, 2009. "Estimating spatial covariance using penalised likelihood with weighted penalty," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 925-942.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:925-942
    DOI: 10.1080/10485250903023632
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    Cited by:

    1. Trevor J. Hefley & Mevin B. Hooten & Ephraim M. Hanks & Robin E. Russell & Daniel P. Walsh, 2017. "The Bayesian Group Lasso for Confounded Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(1), pages 42-59, March.
    2. Lee, Wonyul & Liu, Yufeng, 2012. "Simultaneous multiple response regression and inverse covariance matrix estimation via penalized Gaussian maximum likelihood," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 241-255.
    3. Zareifard, Hamid & Rue, Håvard & Khaledi, Majid Jafari & Lindgren, Finn, 2016. "A skew Gaussian decomposable graphical model," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 58-72.
    4. Marwan Al-Momani & Abdulkadir A. Hussein & S. E. Ahmed, 2017. "Penalty and related estimation strategies in the spatial error model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(1), pages 4-30, January.

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