The problem of assessing a parametric regression model in the presence of spatial correlation is addressed in this work. For that purpose, a goodness-of-fit test based on a \(L_2\)-distance comparing a parametric and nonparametric regression estimators is proposed. Asymptotic properties of the test statistic, both under the null hypothesis and under local alternatives, are derived. Additionally, a bootstrap procedure is designed to calibrate the test in practice. Finite sample performance of the test is analyzed through a simulation study, and its applicability is illustrated using a real data example.

中文翻译：

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具有空间相关误差的回归模型的拟合优度检验

在这项工作中解决了在存在空间相关性的情况下评估参数回归模型的问题。为此，提出了基于\（L_2 \）距离的拟合优度检验，该参数比较了参数回归估计量和非参数回归估计量。在原假设和局部替代条件下，得出检验统计量的渐近性质。此外，还设计了引导程序以在实践中校准测试。通过模拟研究分析了测试的有限样本性能，并通过一个真实的数据示例说明了其适用性。