Variable Selection For Spatial Autoregressive Model And It's Application

In recent years,spatial autoregressive model has been one of the hot topics in statistics.In many real data analysis,researchers collect the data with some location information,thus,which have the relationship of spatial correlation.In addition,in order to reduce the model bias,many explanatory variables are generally collected and need to be assessed during the initial analysis.However,adding some noninformative variable would reduce the model bias as well as increae predicition error.Therefore,deciding which covariates to keep in the final statistical model and which variables are noninformative is practically interesting for spatial autoregressive model.To achieve simultaneous variable selection and estimation of the parameter,we use profile quasi-maximum likelihood estimation of spatial autoregressive models to obatian the estimation of the regressive parameter and spatial parameter under full model.Then,we construct a new objective function from the predicitive view,and obtain the spare estimator of the regressive parameter via penalizing the new objective function.Finite sample performance of the proposed variable selection procedures is assessed by Monte Carlo simulation studies,and the simulation results show that the proposed variable selection could identificate the zero and non-zero coefficients.Finally,we use the Boston housing price data to illustrate the practicability of the resulting method.We found that some imporant variable is noninformative during analysising the Boston housing price data.Consequently,we develop the partial linear additive spatial autoregressive model.To complete the estimation procedure,we first approximate the additive component of the proposed model by polynomial spline.Then,obtain the estimator of model parameters via profiling likelihood.Simulation study shows high efficiency of the proposed estimator.The method is applied to a real data analysis of the well known Boston housing data and reveal the nonlinear effects between the response and cetain covariates.