本文關(guān)鍵詞：廣義度量矩陣測(cè)度方法研究及在信用評(píng)級(jí)中的應(yīng)用　出處：《哈爾濱工業(yè)大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 廣義度量矩陣 信用評(píng)級(jí) 距離度量函數(shù) 樣本間差異

【摘要】：信用評(píng)級(jí)問題的主要研究?jī)?nèi)容是評(píng)級(jí)模型的構(gòu)建,常用的信用評(píng)級(jí)模型并不一定具有普適性,通常存在一些問題。因此,構(gòu)建一個(gè)更具有科學(xué)性與合理性的模型是很有意義的。信用評(píng)級(jí)結(jié)果間存在差異,而距離通常被用來度量?jī)深悩颖鹃g的差異程度,同時(shí)也作為樣本分類的標(biāo)準(zhǔn)。在研究中,基于單位矩陣的歐氏距離和基于協(xié)方差矩陣的馬氏距離是應(yīng)用范圍最廣的兩種度量尺度,然而這兩種距離在應(yīng)用中存在很多不合適的情況。因此,找到一個(gè)能夠更合理地描述差異性的距離或者估算出廣義距離定義中的度量矩陣,在本文的研究中,我們直接用度量矩陣去測(cè)度某一類問題或樣本間的距離是一項(xiàng)有意義的探索,同時(shí)對(duì)度量矩陣進(jìn)行特征值分解,得出的結(jié)論可以更客觀地表述各指標(biāo)的重要性,避免了像很多研究方法中賦權(quán)自身帶有的主觀性。本文在關(guān)于廣義度量矩陣測(cè)度方法的研究中,主要分為以下兩個(gè)方面:一是已知各樣本間的差異,直接利用樣本集中各樣本間的差異來估計(jì)度量矩陣并以此來構(gòu)建評(píng)級(jí)模型;二是利用極值理論,以樣本集合中已知分類結(jié)果的各樣本與各類別指標(biāo)變量均值的最優(yōu)距離為評(píng)判標(biāo)準(zhǔn),測(cè)算度量矩陣并以此來構(gòu)建評(píng)級(jí)模型。本文在推導(dǎo)兩類廣義度量矩陣的測(cè)度公式的研究中,主要是利用廣義距離度量公式的展開式,基于兩個(gè)研究方向?qū)Χ攘烤仃囘M(jìn)行測(cè)算并給出完備的數(shù)學(xué)推導(dǎo)過程。采用的數(shù)學(xué)方法主要是矩陣代數(shù)的方法,具體到兩種研究方向,分別采用了矩陣最小二乘法以及拉格朗日乘子法。利用完備的數(shù)學(xué)推導(dǎo)可以證明度量矩陣表達(dá)式的科學(xué)性與合理性,并且將通過推導(dǎo)出的測(cè)度公式構(gòu)建的評(píng)級(jí)模型應(yīng)用于企業(yè)主體信用評(píng)級(jí)問題,通過實(shí)證檢驗(yàn),說明新模型的精度較高,適合應(yīng)用于信用評(píng)級(jí)問題的研究。
[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.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：F830.5;F224

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本文編號(hào)：1338435