空间单指标自回归模型的估计与检验
发布时间：2018-09-08 19:53
【摘要】：作为计量经济学的一个新的分支学科,空间计量经济学在近些年来发展迅速,越来越多的学者对其理论和应用进行了深入的探讨。空间计量经济学的基础是空间自回归模型,空间自回归模型现已成为应用最为广泛的建模方法。但是,空间自回归模型属于参数模型,在实际数据产生机制下,参数模型可能不能很好地解释实际数据。于是为了更好的探索变量间的复杂关系,非参数与半参数模型在计量经济学和统计学领域都得到了重视,但是基于非参数与半参数模型分析空间数据的研究结果却相对较少。为了能更好的解释数据和避免“维数灾难”,本文首先提出空间单指标自回归模型,空间单指标自回归模型是参数空间自回归模型和半参数单指标回归模型的推广模型,正因为它不仅具有独特的降维特性又能很好的拟合空间数据,对其进行研究将是一件十分有意义的事情。其次,由于局部线性是一种比较好的近似未知函数的方法,M-估计又是一种比较稳健的估计方法,因此本文基于局部线性光滑和M-估计法相结合的两阶段方法及极大似然估计方法对空间单指标自回归模型进行估计,进而基于Bootstrap对该模型的参数与非参数部分进行检验。最后通过数值模拟检验所提方法的有效性。
[Abstract]:As a new branch of econometrics, spatial econometrics has developed rapidly in recent years. More and more scholars have deeply discussed its theory and application. Spatial autoregressive model is the basis of spatial econometrics. Spatial autoregressive model has become the most widely used modeling method. However, the spatial autoregressive model belongs to the parameter model. Under the actual data generation mechanism, the parametric model may not be able to explain the actual data well. Therefore, in order to better explore the complex relationship between variables, non-parametric and semi-parametric models have been attached importance in econometrics and statistics, but the results of spatial data analysis based on non-parametric and semi-parametric models are relatively few. In order to better interpret the data and avoid the "dimension disaster", this paper first puts forward the spatial single index autoregressive model, which is a generalized model of parametric space autoregressive model and semi-parametric single index regression model. Because it not only has the special dimension reduction characteristic but also can fit the spatial data well, it will be very meaningful to study it. Secondly, because local linearity is a better approach to approximate unknown functions, M- estimation is also a more robust estimation method. Therefore, this paper estimates the spatial single-parameter autoregressive model based on the two-stage method of local linear smoothing and M- estimation, and the maximum likelihood estimation method, and then tests the parametric and non-parametric parts of the model based on Bootstrap. Finally, the effectiveness of the proposed method is verified by numerical simulation.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1
，
本文编号：2231528
[Abstract]:As a new branch of econometrics, spatial econometrics has developed rapidly in recent years. More and more scholars have deeply discussed its theory and application. Spatial autoregressive model is the basis of spatial econometrics. Spatial autoregressive model has become the most widely used modeling method. However, the spatial autoregressive model belongs to the parameter model. Under the actual data generation mechanism, the parametric model may not be able to explain the actual data well. Therefore, in order to better explore the complex relationship between variables, non-parametric and semi-parametric models have been attached importance in econometrics and statistics, but the results of spatial data analysis based on non-parametric and semi-parametric models are relatively few. In order to better interpret the data and avoid the "dimension disaster", this paper first puts forward the spatial single index autoregressive model, which is a generalized model of parametric space autoregressive model and semi-parametric single index regression model. Because it not only has the special dimension reduction characteristic but also can fit the spatial data well, it will be very meaningful to study it. Secondly, because local linearity is a better approach to approximate unknown functions, M- estimation is also a more robust estimation method. Therefore, this paper estimates the spatial single-parameter autoregressive model based on the two-stage method of local linear smoothing and M- estimation, and the maximum likelihood estimation method, and then tests the parametric and non-parametric parts of the model based on Bootstrap. Finally, the effectiveness of the proposed method is verified by numerical simulation.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1
，
本文编号：2231528
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