Statistical Analysis of Spatial Dynamic Pattern in Spatial Data Analysis

In this thesis, inspired by the Boston House Price data, we propose a semiparametric spatial dynamic model, that extends the ordinary spatial autoregressive models to accommodate the effects of some covariates associated with the House price. A profile likelihood-based estimation procedure is proposed and the asymptotic normality of the proposed estimators are derived. We also investigate the connection between cross-validation method and AIC/BIC methods in the semiparametric family. In the proposed model, it is easier to apply the AIC/BIC method than the $cross-validation$ method. We illustrate how to identify the parametric/nonparametric components in the proposed semiparametric model. We also show how many unknown parameters an unknown bivariate function amounts to, and propose an AIC/BIC nonparametric model selection. Simulation studies are conducted to examine the performance of the proposed methods, and their results show that the methods work very well. Finally, we apply the proposed methods to analyze the Boston House Price data, which lead to some interesting findings.Although, the proposed model and methodology are stimulated by the Boston House Price data, they could be widely used in many other scientific problems.