Combining Robustness with Efficiency in the Estimation of the Variogram
Combining Robustness with Efficiency in the Estimation of the Variogram
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DOI：
10.1007/s11004-010-9308-3
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发表时间：
2011-04
影响因子：
2.6
通讯作者：
H. Miranda;Manuela Souto de Miranda-Manuela-Souto de Miranda-147605777
中科院分区：
文献类型：
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作者：
H. Miranda;Manuela Souto de Miranda-Manuela-Souto de Miranda-147605777
在本文中，我们提出了一种新的方法估计的变异函数，它结合了鲁棒性和效率下的内在平稳地质统计过程。该方法首先使用鲁棒估计器来获得变异函数的离散估计并控制可能存在的非典型观测。当模型拟合中使用的点数与参数数相同时，普通最小二乘法和广义最小二乘法是渐近等价的。因此，下一步是通过普通最小二乘法拟合变差函数，仅使用几个离散估计值。然后用不同的点子集重复该过程几次，这产生一系列变差函数估计值。最终估计值是变异函数参数的多个估计值的中位数。建议的估计量将被称为多重变异函数估计量。这个过程确保了一个全局鲁棒估计，这是更有效的比其他强大的建议。在假设的相依结构下，我们证明了多重变差函数估计是相合的且渐近正态分布。仿真研究证实了新方法与现有的其他方法相比具有一些优点。
In the present paper, we propose a new method for the estimation of the variogram, which combines robustness with efficiency under intrinsic stationary geostatistical processes. The method starts by using a robust estimator to obtain discrete estimates of the variogram and control atypical observations that may exist. When the number of points used in the fit of a model is the same as the number of parameters, ordinary least squares and generalized least squares are asymptotically equivalent. Therefore, the next step is to fit the variogram by ordinary least squares, using just a few discrete estimates. The procedure is then repeated several times with different subsets of points and this produces a sequence of variogram estimates. The final estimate is the median of the multiple estimates of the variogram parameters. The suggested estimator will be called multiple variograms estimator. This procedure assures a global robust estimator, which is more efficient than other robust proposals. Under the assumed dependence structure, we prove that the multiple variograms estimator is consistent and asymptotically normally distributed. A simulation study confirms that the new method has several advantages when compared with other current methods.