A new method based on distances for modeling continuous random data in Gaussian random fields is presented. In non-stationary cases in which a trend or drift is present, dealing with information in regionalized mixed variables (including categorical, discrete and continuous variables) is common in geosciences and environmental sciences. The proposed distance-based method is used in a geostatistical model to estimate the trend and the covariance structure, which are key features in interpolation and monitoring problems. This strategy takes full advantage of the information at hand due to the relationship between observations, by using a spectral decomposition of a selected distance and the corresponding principal coordinates. Unconditional simulations are performed to validate the efficiency of the proposed method under a variety of scenarios, and the results show a statistical gain when compared with a more traditional detrending method. Finally, our method is illustrated with two applications: earth’s average daily temperatures in Croatia, and calcium concentration measured at a depth of 0–20 cm in Brazil. Supplementary materials accompanying this paper appear online.

中文翻译：

---

一种基于距离的趋势空间预测方法

提出了一种基于距离对高斯随机场中连续随机数据进行建模的新方法。在存在趋势或漂移的非平稳情况下，处理区域化混合变量（包括分类变量、离散变量和连续变量）中的信息在地球科学和环境科学中很常见。提出的基于距离的方法用于地统计模型来估计趋势和协方差结构，这是插值和监测问题的关键特征。由于观测之间的关系，该策略通过使用选定距离和相应主坐标的光谱分解，充分利用了手头的信息。执行无条件模拟以验证所提出方法在各种情况下的效率，与更传统的去趋势方法相比，结果显示了统计增益。最后，我们的方法通过两个应用进行了说明：克罗地亚的地球日平均温度和巴西在 0-20 厘米深度处测量的钙浓度。本文随附的补充材料出现在网上。