扭曲测量误差数据下分位数回归模型的统计分析

发布时间：2018-01-24 01:17

本文关键词： 扭曲测量误差数据混杂变量分位数回归相对渐近效率　出处：《深圳大学》2017年硕士论文　论文类型：学位论文

【摘要】：近年来,随着科学技术的迅速发展,我们发现在越来越多的学科当中,测量误差数据开始频繁出现,如在医疗健康,金融经济,工程测量等等诸多方面的应用研究中。一般情况下存在两种测量误差数据模型:一种是有可加形式的测量误差数据模型,这种模型也包括了传统的测量误差模型;另一种是有相乘结构的测量误差数据模型,我们称作扭曲测量误差模型。在本文中,我们主要研究的是扭曲测量误差模型。这种测量误差数据有以下特征:第一,我们所感兴趣的主要变量无法观测或测量得到;第二,这些主要变量(模型中的响应变量和协变量)被一些常见的可被观测到的混杂变量的某种形式的函数所扭曲,而函数形式通常又是未知的。因此,对这类的扭曲测量误差数据建立一个分位数回归模型是本文的主要研究工作。对于扭曲测量误差数据建模,已有很多研究给出相当有价值的建议,本文在这些基础上尝试用一种新的方法—分位数回归估计,来对这类数据建模,以期达到更好的效果。在对那些含有误差的变量标准化处理后,本文研究了分位数回归估计方法来给这些变量建模。随后,我们研究了估计量的渐近性质,并且与最小二乘回归估计比较了相对渐近效率。最后,本文通过模拟来验证所提出方法的估计效果,并用所提出的方法与程序分析一组实际数据集。
[Abstract]:In recent years, with the rapid development of science and technology, we found that in more and more disciplines, measurement error data began to appear frequently, such as medical health, financial economy. Generally, there are two kinds of measurement error data models: one is the measurement error data model with additive form. This model also includes the traditional measurement error model. The other is the measurement error data model with multiplicative structure, which is called the distortion measurement error model in this paper. We mainly study the distortion measurement error model, which has the following characteristics: first, the main variables we are interested in can not be observed or measured; Second, these main variables (response variables and covariables in the model) are distorted by some form of function of some common observable hybrid variable, which is usually unknown. Establishing a quantile regression model for this kind of distortion measurement error data is the main research work in this paper. There are many valuable suggestions for the distortion measurement error data modeling. In this paper, we try to use a new method, quantile regression estimation, to model this kind of data in order to achieve better results. In this paper, the quantile regression estimation method is studied to model these variables. Then, we study the asymptotic properties of the estimator, and compare the relative asymptotic efficiency with the least square regression estimation. In this paper, the estimation effect of the proposed method is verified by simulation, and a set of actual data sets is analyzed by the proposed method and program.
【学位授予单位】：深圳大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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