时空加权回归模型的估计及变量选择

发布时间：2018-11-05 11:33

【摘要】：模型选择的准确性对系数估计、数据分析、统计决策都有着至关重要的作用。近些年来,许多学者针对模型建立中解释变量的准确选取提出了不同的方法,并在应用中有着不错的效果。但是,随着数据生成机制复杂程度的增加,简单的变系数模型已经不能满足数据变化特征的要求,那么在建立模型时就需要考虑更多影响数据变化的因素。针对具有时空特点的数据,时空加权回归模型(GTWR)通过把时间和地理位置的因素纳入到解释变量的系数中给出了一个合理解释,GTWR模型可以形象的分析变量间的相依关系,而且从系数函数的变化也能清晰的反映数据分布的时空特征。然而,和其他简单模型一样,GTWR模型中解释变量的准确选取对模型的精度也是至关重要的。因此本文将对GTWR模型的系数表示、变量选择的方法以及性质、模拟实证方面进行研究。首先,基于最小二乘原理,通过利用样条基函数,给出了具有时空特点的变系数函数的逼近形式,样条基函数的局部支撑性、单位分解性等良好的性质在进行变量选择的过程中使得理论方法的推导更具规律性,并且样条基函数的局部支撑性使得系数估计值更具灵活性。其次,目标函数在最小二乘目标函数的基础上结合惩罚项,不仅对系数函数做出估计,而且对与响应变量无关的解释变量所对应的系数函数进行压缩,保留重要变量,剔除与响应变量不相关的解释变量,确定精确的模型形式。同时,为了说明方法的合理性,给出相关重要定理的证明,结论说明研究方法是合理的。最后,在模拟实证部分,本文首先对三种不同的变量选择方法在不同样本数量的条件下做模拟分析,结果表明,SCAD方法在样本数量增加的情况下对模型的系数函数的估计最准确,而且模型误差也最小。其次基于GTWR模型,应用气象数据对我国70个城市的空气质量分别从时间和空间的跨度上做了实例分析,研究结果表明,不管是时间因素还是空间因素,都影响着解释变量对响应变量的贡献比重,呈现一定的时空非平稳性,并且得到的系数估计值在不同时间点和不同区域都有着较好的拟合效果。
[Abstract]:The accuracy of model selection plays an important role in coefficient estimation, data analysis and statistical decision. In recent years, many scholars have put forward different methods for accurate selection of explanatory variables in model building, and have good results in application. However, with the increasing complexity of the data generation mechanism, the simple variable coefficient model can no longer meet the requirements of the data change characteristics, so more factors affecting the data change should be taken into account in the establishment of the model. For the spatio-temporal data, the spatio-temporal weighted regression model (GTWR) gives a reasonable explanation by incorporating the factors of time and geographical location into the coefficients of the explanatory variables. The GTWR model can vividly analyze the dependent relationships between variables. And the change of coefficient function can clearly reflect the spatial and temporal characteristics of data distribution. However, as with other simple models, accurate selection of explanatory variables in the GTWR model is also crucial to the accuracy of the model. Therefore, this paper will study the coefficient representation of GTWR model, the methods and properties of variable selection, and the simulation demonstration. Firstly, based on the principle of least squares, the approximation form of variable coefficient function with space-time characteristic and the local support of spline basis function are given by using spline basis function. The good properties such as unit decomposition make the derivation of theoretical methods more regular in the process of variable selection and the local support of spline basis functions makes the estimation of coefficients more flexible. Secondly, based on the least square objective function, the objective function not only estimates the coefficient function, but also compresses the coefficient function corresponding to the explanatory variable independent of the response variable. The exact model form is determined by eliminating the explanatory variables which are not related to the response variables. At the same time, in order to explain the rationality of the method, the relevant important theorems are proved, and the conclusion shows that the research method is reasonable. Finally, in the part of simulation, this paper first analyzes three different methods of variable selection under the condition of different number of samples, and the results show that, SCAD method is the most accurate method to estimate the coefficient function of the model when the number of samples increases, and the error of the model is the least. Secondly, based on GTWR model, the air quality of 70 cities in China is analyzed from time and space span by using meteorological data. The results show that, whether it is time factor or space factor, Both of them affect the contribution of the explanatory variables to the response variables and present a certain spatio-temporal nonstationarity and the estimated coefficients have better fitting effect at different time points and different regions.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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