Inspection Of The Two Types Of Statistical Models

In recent years, the semi-parametric econometrics and spatial econometrics as econometric forefront have been researched deeply in the theory and applications.Additive model extended as a general non-parametric regression model has been paid the attention by the econometricians and statisticians, but there is no study about testing serial correlation for the model. However, in practice, especially when analyzing the time series data, testing serial correlation of the model error is a very basic issue of serial correlation in residual errors,because the estimates calculated through the least squares method can not be effective, even in some cases are mismatched. This paper will study the serial correlation of the additive model, we will deduce an F-test statistic and study its asymptotic properties. We will also verify the validity of the F-test statistic by numerical simulation. The simulation results show that this testing statistic is suited for the large samples.Spatial panel data model is the extension of the panel data model and spatial data model, this model is often used in practice, and therefore it is very necessary to test spatial heterogeneity for spatial panel data model. Based on the Lagrange multiplier methods, we deduce the parameter significance testing statistic for the two-way spatial error correlation random effects panel data model, respectively, we deduce the Lagrange test statistics on the assumption that one or both effects exist.We will provide a testing spatial heterogeneity method for spatial panel data model. The results show that the statistical inference based on the likelihood function, though do not need to estimate the variance, the asymptotic distribution of the statistic is not easy to be proved, when deducing the testing statistics in high dimensions.