回归分析中异常值诊断方法的比较研究

发布时间：2018-04-29 04:20

本文选题：异常值 + 回归分析　；参考：《兰州商学院》2014年硕士论文

【摘要】：回归分析是一种统计学上分析数据的方法，其目的在于了解两个或多个变量间是否相关、相关方向与强度，并建立数学模型以便观察特定变量来预测、控制研究者感兴趣的变量。经典的线性回归模型理论创立以来，被广泛应用于自然科学与社会科学等许多领域中，并取得许多成果。但是应用回归分析的时候经常存在异常值，这些异常值会直接影响到我们所做的回归模型与现实情况是否能很好地拟合、以及参数估计的精确程度、模型的稳定程度等一系列涉及到回归分析本身的问题。因此，对异常值的诊断和处理是一个兼具理论意义和实际意义的问题。异常值的诊断方法一直备受学者们的关注，但是迄今为止，还没有一种标准或者广泛适用的方法。本文对应用较为广泛的两类诊断异常值的方法——基于LS的和基于稳健回归的诊断方法做了一定的介绍。论文先简要介绍了前一类方法，，并对该类方法进行了总结，指出各种方法在应对不同异常值诊断时存在的缺陷，进而引出后一类方法，本文的重点也在于研究回归分析中稳健的异常值诊断方法，通过模拟，研究各种方法在异常值诊断中的效率，并且将几种常用稳健诊断方法的效率进行比较，探讨不同异常值出现的情况下，最为有效的诊断方法。论文共分六部分，首先是绪论部分，主要给出回归分析中有关异常值的综述总结；第二部分主要介绍有关异常值的定义、分类及各种异常值对回归分析结果的影响；第三部分主要讨论目前对回归分析中异常值诊断和处理的方法以及各种方法的适用性和不足；第四部分通过模拟出各种情况的异常值，在简单回归模型和多元回归模型中分别采用常用的几种异常值诊断方法，将各个方法的诊断效率进行比较；第五部分给出真实案例并进行分析；最后介绍本文的结论、不足及未来的工作。
[Abstract]:Regression analysis is a statistical method of analyzing data to understand whether two or more variables are correlated, the direction and intensity of the correlation, and to establish mathematical models to observe specific variables to predict. Controls variables of interest to researchers. Since the establishment of classical linear regression model theory, it has been widely used in many fields, such as natural science and social science, and many achievements have been made. However, when applying regression analysis, there are often outliers, which will directly affect whether the regression model we make can fit well with the reality and the accuracy of parameter estimation. The stability of the model is a series of problems related to regression analysis itself. Therefore, the diagnosis and treatment of outliers is a problem of both theoretical and practical significance. The diagnostic methods of outliers have been paid much attention by scholars, but so far, there is not a standard or widely applicable method. In this paper, two widely used methods for diagnosing outliers are introduced, which are based on LS and robust regression. In this paper, the former method is briefly introduced, and the method is summarized. The defects of each method in dealing with different outliers diagnosis are pointed out, and then the latter kind of method is introduced. The emphasis of this paper is also to study the robust outliers diagnosis method in regression analysis. Through simulation, the efficiency of various methods in outlier value diagnosis is studied, and the efficiency of several commonly used robust diagnostic methods is compared. The most effective diagnostic method is discussed in the case of different outliers. The thesis is divided into six parts, the first part is the introduction part, mainly gives the summary of the abnormal value in the regression analysis, the second part mainly introduces the definition of the abnormal value, the classification and the influence of all kinds of abnormal value on the result of regression analysis. The third part mainly discusses the current methods of diagnosing and dealing with outliers in regression analysis, and the applicability and deficiency of various methods. In the fourth part, the outliers of various situations are simulated. In the simple regression model and the multivariate regression model, we use several commonly used outlier diagnosis methods to compare the diagnostic efficiency of each method; the fifth part gives the real case and analysis; finally, the conclusion of this paper is introduced. Insufficient and future work.
【学位授予单位】：兰州商学院
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224

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