Christensen William F
Department of Statistics, Brigham Young University, Provo, Utah 84602, USA.
Biometrics. 2011 Sep;67(3):947-57. doi: 10.1111/j.1541-0420.2011.01563.x. Epub 2011 Mar 1.
When predicting values for the measurement-error-free component of an observed spatial process, it is generally assumed that the process has a common measurement error variance. However, it is often the case that each measurement in a spatial data set has a known, site-specific measurement error variance, rendering the observed process nonstationary. We present a simple approach for estimating the semivariogram of the unobservable measurement-error-free process using a bias adjustment of the classical semivariogram formula. We then develop a new kriging predictor that filters the measurement errors. For scenarios where each site's measurement error variance is a function of the process of interest, we recommend an approach that also uses a variance-stabilizing transformation. The properties of the heterogeneous variance measurement-error-filtered kriging (HFK) predictor and variance-stabilized HFK predictor, and the improvement of these approaches over standard measurement-error-filtered kriging are demonstrated using simulation. The approach is illustrated with climate model output from the Hudson Strait area in northern Canada. In the illustration, locations with high or low measurement error variances are appropriately down- or upweighted in the prediction of the underlying process, yielding a realistically smooth picture of the phenomenon of interest.
在预测观测到的空间过程的无测量误差分量的值时，通常假定该过程具有共同的测量误差方差。然而，空间数据集中的每个测量值往往具有已知的、特定位置的测量误差方差，这使得观测到的过程是非平稳的。我们提出了一种简单的方法，通过对经典半变异函数公式进行偏差调整来估计不可观测的无测量误差过程的半变异函数。然后，我们开发了一种新的克里金预测器，用于过滤测量误差。对于每个站点的测量误差方差是感兴趣过程的函数的情况，我们推荐一种也使用方差稳定变换的方法。通过模拟展示了异方差测量误差过滤克里金（HFK）预测器和方差稳定HFK预测器的性质，以及这些方法相对于标准测量误差过滤克里金的改进。使用加拿大北部哈德逊海峡地区的气候模型输出对该方法进行了说明。在该示例中，在对潜在过程的预测中，具有高或低测量误差方差的位置被适当地降权或升权，从而得到了感兴趣现象的实际平滑图像。
