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An example of inconsistent MLE of spatial covariance parameters under increasing domain asymptotics

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  • Zhang, Tonglin

Abstract

Asymptotic properties of estimators of covariance parameters in spatial statistics are commonly considered under the frameworks of increasing domain and fixed domain asymptotics, respectively. Although inconsistency is a general conclusion under the framework of fixed domain asymptotics, it is generally believed that consistency should generally hold under the framework of increasing domain asymptotics. This article provides an example in which the maximum likelihood estimator (MLE) of covariance parameters is still inconsistent under the framework of increasing domain asymptotics. Therefore, consistency may still be a problem under the framework of increasing domain asymptotics.

Suggested Citation

  • Zhang, Tonglin, 2017. "An example of inconsistent MLE of spatial covariance parameters under increasing domain asymptotics," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 108-113.
    • Handle: RePEc:eee:stapro:v:120:y:2017:i:c:p:108-113
    DOI: 10.1016/j.spl.2016.10.002
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    References listed on IDEAS

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    1. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    2. Ying, Zhiliang, 1991. "Asymptotic properties of a maximum likelihood estimator with data from a Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 280-296, February.
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