| In the process of economic development research,people will pay attention to such a phenomenon:Individual economic indicators will not only be affected by their own conditions and factors,but also related to the surrounding environment and factors.That is to say,some economic phenomena or attributes of region are related to the same phenomena or attributes of adjacent regions.Therefore,in the process of collecting data,according to previous experience,researchers not only need to obtain various influencing factors that can affect the economic phenomena or attribute of region,that is explanatory variables or independent variables in Econometrics and Statistics,but also collect data that can show economic phe-nomena or attributes in adjacent areas in the same period.In the past,due to the influence of technical reasons,a large number of data collection may be diffi-cult to collect or store.Now with the rapid development of computer technology and network,it is easier to collect and store data,so that researchers can better apply data.Such data often contain information about the geographical location of regions or individuals,which can not be ignored in the study of regional econ-omy.This is also the origin of spatial statistics.Spatial Statistics includes spatial geography,spatial image generation,spatial economics.In Econometrics,Spatial Econometrics derives from the research of spatial-dependent data.Spatial econometrics is one branch of the Econometrics,Since the 1970s and 1980s,there have been many branches of spatial econometric mod-els,which have attracted the attention of econometric economists and statistician-s.The most basic and most studied model is spatial autoregressive model(SAR model):Y_n=?WY_n+U_n,and Y_n=?WY_n+X?+U_n.It can be effectively deal with economic phenomena with spatial correlation.These models shoe that the in-terpreted variables are not only related to the interpreted variables in the regions,but also to the interpreted variables in the adjacent regions.And this correlation can be expressed by the specific statistical index”Moran'I”.In general statistical models,there is a phenomenon that some explanatory variables are not”linear”way appears in the model,but in the form of nonparametric,resulting in semi-parametric statistical model,and in the spatial econometric model.In this paper,three models are researched:linear spatial autoregressive model;partially linear spatial autoregressive model and partially linear additive spatial autoregressive model.In statistical modeling,in order to reduce the deviation of the model,people often rolling to many explanatory variables as possible.Although it can be reduce the deviation of the model,there will be another problem.The increase of ex-planatory variables will increase the parameters that need to be estimated,which will lead to increasing of variance of the model.In order to solve this problem,that is,to reduce the deviation and variance of the model at he same time,it is neces-sary to find a suitable balance point,and the effective method is to consider the problem of variable selection in statistical model or the problem of the selecting statistical model.Variable selection methods have appeared in many statistical models,but they are seldom used in spatial econometric models.It is also the work of this paper to apply variable selection to the spatial linear autoregressive model in order to obtain the optimal spatial econometric model.Above is the problem to be studied in this paper,from which we can perceive the significance of its work.The main research of this paper include the following aspects:For the classical linear spatial autoregressive model,when the dimension of parameters tends to be infinite,a new penalty parameter estimation is proposed based on the non-convex penalty likelihood estimation method.Under certain regular conditions,it is proved that when the dimension of parameters increas-es simultaneously with the sample size,but the increase of dimension is slower than that of sample size,it satisfies when n??,p_n??,that p_n~4/n?0.The parameter estimates given in this way converge to the real parameters(i.e.existence)according to probability,and also have sparsity and asymptotic nor-mality.The simulation results prove that this estimation method can achieve better results,and the actual data analysis proves that for the case of parame-ter dimension divergence,decisive explanatory variables can be selected.For a type of semi-parametric model,partially linear spatial autoregressive model,this paper does the following work:Firstly,for the nonparametric part of the model,the more universal sieve method is used to give the estimation expression of the function part.Then for the linear spatial autoregressive part of the model,when the spatial lag term is endogenous,the expression of the parameter estimation of the linear part is given by using the instrumental variable method.At the same time,under some regular conditions,it is proved that the finite dimension param-eter estimation vector of the linear part has asymptotic normality,and for the sieve estimation of the nonparametric function,the optimal convergence rate is found.The finite sample properties of the estimates are obtained by Monte Carlo simulation.Finally,this estimation method is applied to the analysis of classical Boston house price data,which proves the superiority and practicability of the proposed estimation.For the more complex semi-parametric model-partial linear additive spatial autoregressive model,the additive function part of the model is approximated by B-spline basis function,which is transformed into a”linear”form.For the new”linear”model,the quantile regression is used,and the endogenous spatial lag term is solved by the instrumental variable method.Then,under fewer regular conditions,the parameter estimates for the linear part of the model have persis-tent existence,uniform convergence and asymptotic normality.For the additive function part of the model,the uniform convergence rate is given. |
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