广义度量矩阵测度方法研究及在信用评级中的应用

发布时间：2017-12-26 18:47

本文关键词：广义度量矩阵测度方法研究及在信用评级中的应用　出处：《哈尔滨工业大学》2015年硕士论文　论文类型：学位论文

【摘要】：信用评级问题的主要研究内容是评级模型的构建,常用的信用评级模型并不一定具有普适性,通常存在一些问题。因此,构建一个更具有科学性与合理性的模型是很有意义的。信用评级结果间存在差异,而距离通常被用来度量两类样本间的差异程度,同时也作为样本分类的标准。在研究中,基于单位矩阵的欧氏距离和基于协方差矩阵的马氏距离是应用范围最广的两种度量尺度,然而这两种距离在应用中存在很多不合适的情况。因此,找到一个能够更合理地描述差异性的距离或者估算出广义距离定义中的度量矩阵,在本文的研究中,我们直接用度量矩阵去测度某一类问题或样本间的距离是一项有意义的探索,同时对度量矩阵进行特征值分解,得出的结论可以更客观地表述各指标的重要性,避免了像很多研究方法中赋权自身带有的主观性。本文在关于广义度量矩阵测度方法的研究中,主要分为以下两个方面:一是已知各样本间的差异,直接利用样本集中各样本间的差异来估计度量矩阵并以此来构建评级模型;二是利用极值理论,以样本集合中已知分类结果的各样本与各类别指标变量均值的最优距离为评判标准,测算度量矩阵并以此来构建评级模型。本文在推导两类广义度量矩阵的测度公式的研究中,主要是利用广义距离度量公式的展开式,基于两个研究方向对度量矩阵进行测算并给出完备的数学推导过程。采用的数学方法主要是矩阵代数的方法,具体到两种研究方向,分别采用了矩阵最小二乘法以及拉格朗日乘子法。利用完备的数学推导可以证明度量矩阵表达式的科学性与合理性,并且将通过推导出的测度公式构建的评级模型应用于企业主体信用评级问题,通过实证检验,说明新模型的精度较高,适合应用于信用评级问题的研究。
[Abstract]:The main research content of the credit rating problem is the construction of the rating model. The common credit rating model is not necessarily universally applicable, and there are usually some problems. Therefore, it is of great significance to build a more scientific and reasonable model. There are differences in credit rating results, and distance is usually used to measure the degree of differences between the two types of samples, and also as a standard for the classification of samples. In the research, the Euclidean distance based on the unit matrix and the Mahalanobis distance based on the covariance matrix are the two most widely applied measurement scales. However, there are many inappropriate situations in the application of the two distances. Therefore, to find a more reasonable description of the difference of the distance or estimate the measurement matrix in the definition of generalized distance, in this study, we directly use the metric to measure a certain class of problems or the distance between samples is a meaningful exploration, while the degree of matrix eigenvalue decomposition and the conclusion can more objectively the importance of each index, to avoid as many research methods with its own subjective weighting. In this paper, a generalized metric matrix measure method, mainly divided into the following two aspects: one is the difference between the known samples, using samples differences between samples to estimate the measurement matrix and to establish the rating model; two is the use of extreme value theory, the optimal mean value of each sample in the set of variables the known classification results with the type of index distance as the criterion, calculation and measurement matrix to construct the evaluation model. In this paper, we derive the measure formula of two kinds of generalized metric matrices, mainly using the expansion formula of generalized distance measure. We calculate the metric matrix based on two research directions and give a complete mathematical deduction process. The mathematical method used mainly is the matrix algebra method, specific to the two research directions, the matrix least square method and the Lagrange multiplier method are used respectively. The use of mathematical derivation of complete metric matrix expressions can prove the scientificity and rationality, and through the measurement of the formulas of rating model is applied to the main corporate credit rating, through empirical testing shows that higher accuracy of the new model, the research applies to credit rating problems.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F830.5;F224

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