模型选择与模型平均方法的研究及其应用

发布时间：2018-03-18 03:25

本文选题：信息准则　切入点：聚类分析　出处：《山东理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：模型选择方法和模型平均方法是目前统计学界研究的前沿问题,这两种方法具有非常广阔的应用前景,因而也具有非常重要的研究意义。模型选择方法与模型平均方法提出的时间都比较早,并且自提出以来一直受到学者们的关注,但是由于种种原因,有关这两种方法的相关研究一直进展比较缓慢。相比较而言,模型选择方法的相关理论研究比较完善,模型平均方法的相关研究则比较少。模型选择和模型平均涉及非常广泛的研究领域,在统计学理论及许多学科中都有切实应用。随着社会和科技的不断进步,有关模型选择和模型平均方法的研究在不断深入与发展,研究学者们也在不断对两种方法进行充实与改进。熟练掌握并运用统计学中的模型选择和模型平均两种方法可以使我们更加容易地选择出准确的统计模型。本文主要研究了模型选择和模型平均方法的相关问题。在模型选择方面主要研究了两方面内容:第一个内容是将模型选择中的相关信息准则与多元统计学中的聚类分析方法相结合,寻找出一种新的聚类方法;另一个内容是将模型选择中的准则函数应用到Poisson回归模型中,找到Poisson回归模型的最佳模型选择方法,并通过案例分析了准则函数在Poisson回归模型中的具体应用。在模型平均方面,主要是基于信息准则创新了模型平均中的组合预测权重问题,提出一种新的模型平均方法,并通过对我国GDP进行组合预测分析,验证了新方法的有效性。
[Abstract]:The model selection method and the model average method are the frontier problems in the field of statistics at present. These two methods have a very broad application prospect. The model selection method and the model average method have been put forward earlier, and have been concerned by scholars since they were put forward, but for a variety of reasons, The research on the two methods has been relatively slow. In comparison, the theoretical research on the model selection method is relatively perfect. Model selection and model average involve a wide range of research fields and have practical applications in statistical theory and many disciplines. With the development of society and science and technology, The research on model selection and model averaging method is being deepened and developed. The researchers are constantly enriching and improving the two methods. Mastering and using the two methods of model selection and model averaging in statistics can make it easier for us to select accurate statistical models. This paper mainly studies the related problems of model selection and model averaging. In model selection, it mainly studies two aspects: the first is to combine the relevant information criterion in model selection with the clustering analysis method in multivariate statistics. A new clustering method is found, and the criterion function in model selection is applied to Poisson regression model to find the best model selection method for Poisson regression model. The concrete application of criterion function in Poisson regression model is analyzed through a case study. In terms of model average, the combination prediction weight problem in model average is innovated based on information criterion, and a new model averaging method is proposed. The effectiveness of the new method is verified by the combination prediction analysis of GDP in China.
【学位授予单位】：山东理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F124

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