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Consistent specification testing under spatial dependence

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Document pages: 56 pages

Abstract: We propose a series-based nonparametric specification test for a regressionfunction when data are spatially dependent, the `space being of a generaleconomic or social nature. Dependence can be parametric, parametric withincreasing dimension, semiparametric or any combination thereof, thus coveringa vast variety of settings. These include spatial error models of varying typesand levels of complexity. Under a new smooth spatial dependence condition, ourtest statistic is asymptotically standard normal. To prove the latter property,we establish a central limit theorem for quadratic forms in linear processes inan increasing dimension setting. Finite sample performance is investigated in asimulation study and empirical examples illustrate the test with real-worlddata.

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