CONSISTENT SPECIFICATION TESTING UNDER SPATIAL DEPENDENCE
提出了一种基于级数的非参数设定检验方法，用于空间依赖数据中回归函数的模型检验，适用于参数、半参数等多种依赖结构，并证明了检验统计量的渐近正态性。
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. Empirical examples illustrate the test with real-world data.