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An asymptotic theory for the nugget estimator in spatial models

Author

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  • Tae Kim
  • Jeong Park
  • Gyu Song

Abstract

The nugget effect is an important parameter for spatial prediction. In this paper, we propose a nonparametric nugget estimator based on the classical semivariogram estimator and describe its large sample distributional properties. Our main results are a central limit theorem and a risk calculation for the estimator when observations are made from a nearly infill domain sampling. From our results, we note that the performance of the estimator depends on the sampling design as well as the choice of bandwidth. In particular, we show that the estimator suffers from strong dependency when d, the dimension of the underlying spatial process, is less than or equal to 2a, a parameter related to the degree of smoothness and dependence of the underlying process. When d>2a, however, the estimator turns out to achieve an optimal rate with an optimal choice of h. We report on the results of simulations to empirically study the estimator.

Suggested Citation

  • Tae Kim & Jeong Park & Gyu Song, 2010. "An asymptotic theory for the nugget estimator in spatial models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 181-195.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:181-195
    DOI: 10.1080/10485250903193997
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    References listed on IDEAS

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    1. Hao Zhang & Dale L. Zimmerman, 2005. "Towards reconciling two asymptotic frameworks in spatial statistics," Biometrika, Biometrika Trust, vol. 92(4), pages 921-936, December.
    2. Lu, Zudi & Tjøstheim, Dag & Yao, Qiwei, 2008. "Spatial smoothing, Nugget effect and infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3145-3151, December.
    3. Huang, Hsin-Cheng & Chen, Chun-Shu, 2007. "Optimal Geostatistical Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1009-1024, September.
    4. Lu, Zudi & Tjostheim, Dag & Yao, Qiwei, 2008. "Spatial smoothing, Nugget effect and infill asymptotics," LSE Research Online Documents on Economics 24133, London School of Economics and Political Science, LSE Library.
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