On the consistent separation of scale and variance for Gaussian random fields
On the consistent separation of scale and variance for Gaussian random fields
复制标题
关于高斯随机场尺度和方差的一致分离
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
E. Anderes
中科院分区：
文献类型：
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作者：
E. Anderes
我们提出了固定域渐近结果，为具有几何各向异性 Matern 自协方差的高斯随机场建立了方差和尺度参数的一致估计，维度 d > 4。当 d 4 时，我们表明可以足够准确地估计主不规则项的系数，以获得第二不规则项的系数的一致估计。然后可以使用这两个系数来分离尺度和方差。我们将结果扩展到估计更一般自协方差函数的方差和几何各向异性的一般问题。我们的结果说明了估计的准确性、随机场的平滑度、观察空间的维度和用于估计的增量数量之间的相互作用。作为推论，我们的结果建立了当 d > 4 时具有不同参数的马特恩高斯随机场的正交性。d = 4 的情况仍然是开放的。
We present fixed domain asymptotic results that establish consistent estimates of the variance and scale parameters for a Gaussian random field with a geometric anisotropic Matern autocovariance in dimension d > 4. When d 4, we show that one can estimate the coefficient on the principle irregular term accurately enough to get a consistent estimate of the coefficient on the second irregular term. These two coefficients can then be used to separate the scale and variance. We extend our results to the general problem of estimating a variance and geometric anisotropy for more general autocovariance functions. Our results illustrate the interaction between the accuracy of estimation, the smoothness of the random field, the dimension of the observation space and the number of increments used for estimation. As a corollary, our results establish the orthogonality of Matern Gaussian random fields with different parameters when d > 4. The case d = 4 is still open.