Diagnosis Of Mixed Spatial Autoregressive Model Problem Of Multiple Outliers

In recent years, with the development of technologies like GIS, GPS and RS,geospatial information of data were getting more and more attention by people. These datausually have spatial autocorrelation which is called the dependence among the data ofdifferent area. Spatial Econometrics is a rapidly developing branch of econometrics inrecent years, which is of great significance for the practical processing a growing numberof data with spatial characteristics. However, outliers are frequently present in spatial data,which may be caused by the use of inappropriate spatial model or some unusual economicphenomena.The mixed regressive-spatial autoregressive(SAR) model is not only an important butalso a widely-used spatial econometric model for modeling data with spatial structure. TheSAR model not only includes the correlation between the independence and the variableof the own area, but also portrays the correlation between the independence and theindependence of the neighbor area. However, it is well known that this spatial econometricmodel is very sensitive to the presence of outliers. When outliers are presented in the dataset, the modeling results drawn from spatial models may results in misleading conclusionsif these outliers are influential. It is thus desirable to find a diagnostic statistic that candetect outliers effectively in spatial econometric models.In this paper, we study the outliers detection problem using score test under mean-shift and variance-weight models. In terms of score method, the testing statistics formultiple outliers are derived under mean-shift and variance-weight outlier modelsrespectively, and the approximate distributions are used to determine the cut-off values. Then we apply the results into first-order spatial autoregressive(FAR) model and get thecorresponding conclusions. We also use the simulation studies to examine theeffectiveness of proposed methodology, including performance of the power and size oftest. Finally a real data of Columbus neighborhood crime is used to verifies theeffectiveness of the proposed methodology.