We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing dimension, semiparametric or any combination thereof, thus covering a vast variety of settings. These include spatial error models of varying types and levels of complexity. Under a new smooth spatial dependence condition, our test statistic is asymptotically standard normal. To prove the latter property, we establish a central limit theorem for quadratic forms in linear processes in an increasing dimension setting. Finite sample performance is investigated in a simulation study, with a bootstrap method also justified and illustrated, and empirical examples illustrate the test with real-world data.

翻译：我们建议,当数据在空间上依赖,“空间”具有一般的经济或社会性质时,对回归功能进行一系列非参数性规格测试,其依赖可以是参数、具有日益增强的尺寸的参数、半参数或任何组合,从而涵盖各种各样的环境,其中包括不同类型和复杂程度的空间错误模型。在新的平稳空间依赖条件下,我们的测试统计是无症状的标准正常。为了证明后一种属性,我们在一个日益扩大的维度环境中为线性进程中的二次形式设定了一个核心限值。在模拟研究中,对Finite样本的性能进行了调查,同时用靴式方法也进行了论证和说明,并用真实世界数据来说明试验的经验实例。