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An asymptotic theory for the nugget estimator in spatial models. (English) Zbl 1182.62186

Summary: The nugget effect is an important parameter for spatial prediction. 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.

MSC:

62M40 Random fields; image analysis
62G20 Asymptotic properties of nonparametric inference
60F05 Central limit and other weak theorems
62G05 Nonparametric estimation
65C60 Computational problems in statistics (MSC2010)
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References:

[1] Chiles J. P., Geostatistics. Modeling Spatial Uncertainty (1999)
[2] Cressie N., Statistics for Spatial Data (revised version) (1994)
[3] DOI: 10.1214/aos/1176349748 · Zbl 0594.62043 · doi:10.1214/aos/1176349748
[4] DOI: 10.1002/9780470386347 · Zbl 1258.62099 · doi:10.1002/9780470386347
[5] Hedge L. V., Statistical Methods for Meta-Analysis (1985)
[6] DOI: 10.1198/016214507000000491 · Zbl 1469.86018 · doi:10.1198/016214507000000491
[7] DOI: 10.1198/108571107X249799 · Zbl 1306.62296 · doi:10.1198/108571107X249799
[8] Lahiri S. N., Sankhya Series A 65 pp 356– (2003)
[9] Lee Y. K., Journal of Korean Statistical Society 35 pp 105– (2006)
[10] DOI: 10.1016/j.spl.2008.06.002 · Zbl 1489.62299 · doi:10.1016/j.spl.2008.06.002
[11] DOI: 10.1007/s11004-008-9184-2 · Zbl 1177.60033 · doi:10.1007/s11004-008-9184-2
[12] Schabenberger O., Statistical Methods for Spatial Data Analysis (2005) · Zbl 1068.62096
[13] DOI: 10.1093/biomet/92.4.921 · Zbl 1151.62348 · doi:10.1093/biomet/92.4.921
[14] Zhang H., Mathematical Geosciences 39 pp 247– (2007)
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