“Consistent specification testing under network dependence” by Dr. Abhimanyu Gupta
University of Essex
We propose a series-based nonparametric specification test for a regression function when data are dependent across a network. Our framework permits network dependence to 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. Furthermore, we also cover models in which network dependence arises directly in outcome variables, possibly with dependence complexity increasing with sample size. Despite being applicable so generally, our test statistic is easy to compute and asymptotically standard normal. To prove the latter property, we present a central limit theorem for quadratic forms in linear processes in an increasing dimension setting that may be of independent interest. Finite sample performance is studied in a simulation study and empirical examples illustrate the test with real-world data.