Specification Test For High-dimensional Partial Lineal Varying Coefficient Spatial Autoregressive Model

The spatial autoregressive model is a common model for analyzing the autocorrelation of spatial data.Comparing with the traditional spatial autoregressive model,the data can be more flexibly fitted by the semi-parametric spatial autoregressive model.Specification test is an important part of the semi-parametric space autoregressive analysis.If the model is set incorrectly,the results obtained based on this will be unreliable or even wrong.Especially with the research hot point of high-dimensional data,the possibility of the model being set incorrectly also increases.Therefore,it is very important to conduct a specification test before statistical analysis of the high-dimensional semi-parametric space autoregressive model.Combining the one-dimensional linear projection of the covariates with the residual empirical process,the thesis proposes a specification test method for the high-dimensional partial linear varying coefficient space autoregressive model.This method is not only suitable for highdimensional covariates,but also avoids the subjective selection of the smooth parameters（such as window width）.In addition,it also covers a variety of different data models.Under certain conditions,we prove that the proposed method is consistent and the test statistic can distinguish the null hypothesis from the alternative hypothesis at the usual parameter convergence speed.Under the limited sample size,we use the bootstrap method to approximate the distribution of the test statistic.The finite sample properties of the proposed test method are studied by Monte Carlo simulation.The results show that under high-dimensional covariates,the experience level of test statistics can be better close to the given test level.The power increases as the sample size increases.Finally,the specification of partial linear spatial autoregressive model is accepted in the Boston housing price data.