城市居民收入与支出的非参数分位数回归估计

发布时间：2018-05-08 22:09

本文选题：分位数回归 + 非参数模型　；参考：《辽宁师范大学》2014年硕士论文

【摘要】：随着统计分析的逐步发展，越来越多的研究学者聚焦于数据建模和统计量分析，因为模型的设定是进行更深层次探究的基础，一个优良的模型，可以对分析对象实现最优拟合，以便更全面更准确的掌握分析对象的特点，这样就可以更深入的研究，并得出切实有效的结论。在形形色色的统计方法中，最小二乘法凭借着自身简洁有效且与想象相符的优势，被广泛应用与参数和非参数模型的研究中。然而，没有一种方法是完美无瑕的，对带有异常值和异方差的数据，由于自身局限性，最小二乘法也存在一定的不足。分位数回归（Quantile Regression）思想的提出，最对这种方法进行了有效的补充与完善。对于估计参数与非参数模型，也显示出了优越的稳定性。本文侧重研究分位数理论、非参数分位数回归模型、局部多项式估计方法以及他们的实际应用，论文的着力于以下几项工作：首先，论文介绍了分位数回归的研究背景，理论的形成和发展过程。可以看出，对分位数的研究过程，从萌芽到成长壮大，其应用领域被学者们不断扩展，说明分位数回归适用于多种领域多种用途的研究。这也从另一个角度说明了对分位数回归问题的研究是很有意义的。其次，，论文详细介绍了本文的理论支持。即分位数回归的定义，基本原理，以及相关的一些性质。对分位数回归进行实用性拓展，找出适合本文研究内容的模型——非参数分位数回归模型，并做出详细介绍。再次，采用非参数模型估计最为常用的方法——局部多项式方法，运用分位数回归技术，对全国230个城市的居民收支情况进行建模与分析，同时列出最小二乘估计的相关结果，通过对比，可以得出：对于数据量大且非常态分布的数据，非参数分位数回归方法是优于普通最小二乘法的，而且可以提供更多的信息，便于得到正确的统计分析结论。最后，本文运用非参数分位数回归技术，得出的结论不仅是对非参数分位数回归应用的扩展，同时也对经济学领域的研究的有益参考。
[Abstract]:With the gradual development of statistical analysis, more and more researchers focus on data modeling and statistics analysis, because the setting of the model is the basis for deeper exploration. A good model can achieve the optimal fitting of the analysis object so that the characteristics of the analysis object can be more comprehensive and more accurate, so that it can be deeper. Research into and draw practical and effective conclusions.
In the various statistical methods, the least square method is widely used in the study of the parameters and non parametric models by virtue of its simplicity and effectiveness and the advantage that it is consistent with imagination. However, there is no one method that is perfect and flawless. For data with abnormal values and heteroscedasticity, the least square method also has a certain degree. The idea of quantile regression (Quantile Regression) is the most effective supplement and perfection of this method. It also shows superior stability for the estimation of parameters and non parametric models. This paper focuses on the study of quantile theory, non parametric quantile regression model, local polynomial estimation method and their actual needs. For use, the thesis focuses on the following tasks:
First, the paper introduces the research background of quantile regression, the formation and development of the theory. It can be seen that the research process of the quantile, from germination to growth and growth, has been expanded by scholars, which indicates that quantile regression is applicable to many fields and many ways of use. This also explains the number of quantiles from another angle. The study of the regression problem is of great significance.
Secondly, the thesis gives a detailed introduction to the theoretical support of this paper, that is, the definition of quantile regression, the basic principle, and some related properties. The practicability of the quantile regression is expanded to find the model which is suitable for the content of this paper, the non parametric quantile regression model, and to make a detailed introduction.
Thirdly, we use the non parametric model to estimate the most commonly used method - local polynomial method and use the quantile regression technique to model and analyze the income and expenditure of the residents in 230 cities. At the same time, the relative results of the least squares estimate are listed. By comparison, we can get the data of large and very distributed data. The parametric quantile regression method is better than the ordinary least squares method, and it can provide more information and facilitate the correct statistical analysis conclusion.
Finally, the conclusion of this paper is not only an extension of non parametric quantile regression, but also a useful reference to the research in the field of economics.

【学位授予单位】：辽宁师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F126;F224

【参考文献】