Model Checking in Partially Linear Spatial Autoregressive Models
针对线性空间自回归模型的设定是否正确，提出了两类基于积分条件矩的非参数检验，无需选择带宽等调节参数，能检测以参数速率收敛的局部备择假设，并通过蒙特卡洛模拟和经济增长收敛实证展示了有效性。
This article proposes two new classes of nonparametric tests for the correct specification of linear spatial autoregressive models based on the “integrated conditional moment” approach. Our test statistics are constructed as continuous functionals of a residual marked empirical process as well as its projected version. We derive asymptotic properties of the test statistics under the null hypothesis, the alternative hypothesis, and a sequence of local alternatives. The proposed tests do not involve the selection of tuning parameters such as bandwidths and are able to detect a broad class of local alternatives converging to the null at the parametric rate n−1/2, with <i>n</i> being the sample size. We also propose a multiplier bootstrap procedure that is computationally simple to approximate the critical values. Monte Carlo simulations illustrate that our tests have a reasonable size and satisfactory power for different types of data-generating processes. Finally, an empirical analysis of growth convergence is carried out to demonstrate the usefulness of the tests.