The analysis of continuously spatially varying processes usually considers two sources of variation, namely, the large-scale variation collected by the trend of the process, and the small-scale variation. Parametric trend models on latitude and longitude are easy to fit and to interpret. However, the use of parametric models for characterizing spatially varying processes may lead to misspecification problems if the model is not appropriate. Recently, Meilán-Vila et al. (TEST 29:728–749, 2020) proposed a goodness-of-fit test based on an \(L_2\)-distance for assessing a parametric trend model with correlated errors, under random design, comparing parametric and nonparametric trend estimates. The present work aims to provide a detailed computational analysis of the behavior of this approach using different bootstrap algorithms for calibration, one of them including a procedure that corrects the bias introduced by the direct use of the residuals in the variogram estimation, under a fixed design geostatistical framework. Asymptotic results for the test are provided and an extensive simulation study, considering complexities that usually arise in geostatistics, is carried out to illustrate the performance of the proposal. Specifically, we analyze the impact of the sample size, the spatial dependence range and the nugget effect on the empirical calibration and power of the test.

连续空间变化过程的分析通常考虑两个变化源，即，由过程趋势收集的大尺度变化和小尺度变化。经度和纬度的参数趋势模型易于拟合和解释。但是，如果模型不适当，则使用参数模型来表征空间变化的过程可能会导致规格不正确的问题。最近，Meilán-Vila等人。（TEST 29：728–749，2020）提出了基于\（L_2 \）的拟合优度检验-在随机设计下用于评估具有相关误差的参数趋势模型的距离，比较参数和非参数趋势估计。本工作旨在使用固定的设计，使用不同的自举算法进行校准，对该方法的行为进行详细的计算分析，其中一种方法包括纠正由直接使用变异函数估计中的残差而引入的偏差的过程。地统计框架。提供了该测试的渐近结果，并进行了广泛的模拟研究，其中考虑了地统计学中通常会出现的复杂性，以说明该提案的性能。具体来说，我们分析了样本量，空间依赖范围和金块效应对经验校准和测试功效的影响。