Residual Kriging for Functional Spatial Prediction of Salinity Curves
Residual Kriging for Functional Spatial Prediction of Salinity Curves
复制标题
用于盐度曲线功能空间预测的残差克里金法
DOI：
10.1080/03610926.2012.753087
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Mateu
中科院分区：
文献类型：
--
作者：
A. Reyes;R. Giraldo;J. Mateu
最近，已经提出了几种对功能数据进行地质统计分析的方法。它们都假定所考虑的空间功能过程是平稳的。然而，在实践中，我们经常会遇到非平稳的函数数据，因为在平均值中存在明显的空间趋势。在这里，我们提出了一种方法，将函数数据的克立格预报器扩展到平均函数在感兴趣区域中不恒定的情况。我们考虑了一种基于用于单变量地质统计学的经典剩余克里格法的方法。我们提出了三个步骤的程序。首先，使用函数回归模型来对平均值进行趋势分析。然后，我们将函数数据的克立格法应用于回归残差，以预测非数据位置的残差曲线。最后，预测曲线由趋势和残差预测之和得到。我们将该方法应用于哥伦比亚加勒比海沿岸Ciénaga Grande de Santa Marta河口记录的21条盐度曲线所对应的盐度数据。进行了交叉验证分析，以跟踪拟议方法的性能。
Recently, several methodologies to perform geostatistical analysis of functional data have been proposed. All of them assume that the spatial functional process considered is stationary. However, in practice, we often have nonstationary functional data because there exists an explicit spatial trend in the mean. Here, we propose a methodology to extend kriging predictors for functional data to the case where the mean function is not constant through the region of interest. We consider an approach based on the classical residual kriging method used in univariate geostatistics. We propose a three steps procedure. Initially, a functional regression model is used to detrend the mean. Then we apply kriging methods for functional data to the regression residuals to predict a residual curve at a non-data location. Finally, the prediction curve is obtained as the sum of the trend and the residual prediction. We apply the methodology to salinity data corresponding to 21 salinity curves recorded at the Ciénaga Grande de Santa Marta estuary, located in the Caribbean coast of Colombia. A cross-validation analysis was carried out to track the performance of the proposed methodology.