Minimum norm quadratic estimation of spatial variograms
Minimum norm quadratic estimation of spatial variograms
复制标题
空间变异函数的最小范数二次估计
DOI：
10.1080/01621459.1987.10478497
复制
发表时间：
1987
期刊：
影响因子：
--
通讯作者：
M. Stein
中科院分区：
文献类型：
--
作者：
M. Stein
摘要空间变异函数是空间相关性的一种度量，其估计是克立格法实现的一个关键问题。我们考虑使用最小范数二次估计的变差函数时，它被指定为一个有限数量的线性参数。我们研究了高斯过程的这种估计量在有界区域内随着观测值数目的增加的渐近行为。基本结论是，我们可以估计一致的参数的那些功能，只有那些功能，有一个不可忽略的影响渐近克里格过程。一般来说，变差函数在相对较短距离上的行为是变差函数中唯一渐近重要的方面。例如，考虑一个高斯过程z（·）在具有未知常数均值的真实的直线上，其中γ（·）被称为过程的半变异函数，θ是未知参数的有限向量。假设，对于0…
Abstract The estimation of spatial variograms, a measure of spatial correlation, is a critical problem in the implementation of kriging, a method for interpolating random fields. We consider the use of minimum norm quadratic estimators of the variogram when it is specified up to a finite number of linear parameters. We investigate the asymptotic behavior of such estimators for Gaussian processes as the number of observations within some bounded region increases. The basic conclusion is that we can estimate consistently those functions of the parameters, and only those functions, that have a nonnegligible impact asymptotically on the kriging procedure. In general, the behavior of the variogram over relatively short distances is the only aspect of the variogram that is asymptotically important. As an example, consider a Gaussian process z(·) on the real line with unknown constant mean and , where γ(·) is known as the semivariogram of the process and θ is a finite vector of unknown parameters. Suppose, for 0...