基于分位数回归技术的删失数据的多重插补

发布时间：2018-03-15 11:06

本文选题：删失数据　切入点：分位数回归　出处：《浙江工商大学》2017年硕士论文　论文类型：学位论文

【摘要】：在很多现实的问题中,由于存在主客观条件的约束,得到的观测数据往往都不是精准的数据,有时只知道感兴趣的数据集中的一些数据的值是小于(大于)等于某个数值或者是介于某个区间段内,这种不完整数据被称之为删失数据(Censored Observation)。存在不同种类的删失数据,比如左删失、右删失和区间删失,另外删失又可以分为固定删失和随机删失。在20世纪70年代末期,对于上面描述的不完整数据的情形,Dempster,Laird和Rubin(1977)提出了一种可以有效估计的EM算法。基于这个算法,Rubin(1977)则提出了通过模拟的思想实现了针对不完整数据的多重插补。此后,Rubin发表了这方面的一系列文章,尔后将其整理并于1987年出版成册,系统地归纳了多重插补法的思想及理论框架。另外分位数回归模型提供了一个半参数化的方法,它可以灵活地处理解释变量与被解释变量之间的关系。即使所研究的数据具有异质性,也能对其进行建模。到目前为止,将分位数回归方法与不完整数据相结合的研究不多,然而分位数回归对处理具有删失的响应变量的情形可以说是非常适合的。因为对误差项没有严格的参数假设,条件均值函数可以是不可识别的。在这篇论文中,着重提出了在响应变量服从固定删失的情形下将分位数回归与多重插补相结合去插补那些被删失数据的一个新方法。将最终得到的结果与其他方法的结果作了一些适当的比较,发现运用此种方法得到的结果基本符合预期。这篇论文的目的主要是提出一个新方法将删失了的数据包括进来并对其进行修补,从而提高估计的效率。本文的主要结构如下:第一章绪论,这里主要介绍了本文的研究背景、研究意义以及文献综述,并告知文章的行文脉络,即研究的思路与框架,另外就是本文研究的主要创新之处。第二章首先介绍了分位数与分位数回归的基本概念、参数估计方法。然后介绍了删失分位数回归的理论及性质。最后着重阐述了多重插补法的一些理论基础。第三章主要针对响应变量存在删失的数据进行插补而引进了一个新方法——基于分位数回归技术的多重插补法,先介绍与它相关的基本理论,再运用这个方法对多种固定删失数据情形进行模拟,并对模拟后的结果进行详细分析。在第四章里面,将提出的方法运用于实际数据下的例子并对结果进行适当的分析。第五章对所提出的方法进行总结,并提出了本文的不足与展望。
[Abstract]:In many practical problems, due to the existence of subjective and objective conditions, the observation data are not accurate, sometimes only know that some data datasets of interest value is less than (greater than) a value equal to or between a range, the incomplete data is called for censored data (Censored Observation). There are different kinds of censored data, such as left censored, right censoring and interval censored failure, also can be divided into fixed censoring and randomly censored and deleted. At the end of the 1970s, for incomplete data on the description of the situation, Dempster, Laird and Rubin (1977) put forward an effective estimation of the EM algorithm. Based on this algorithm, Rubin (1977) is proposed through simulation to realize the multiple imputation for incomplete data. Since then, Rubin has published a series of articles in this area, After the finishing in 1987 and published the book, systematically summarizes the ideological and theoretical framework of multiple imputation. In addition the quantile regression model provides 1.5 methods of parameter, it can flexibly deal with the explanatory variables to explain the relationship between the variables. Even if the data are heterogeneous and can be modeled on it. So far, not much research combining the quantile regression method with incomplete data, however, quantile regression with censored response variable to the situation can be said to be very suitable. Because there is no strict assumption of parameter error, the conditional mean function is not recognized in this paper, put forward in response variables fixed censored cases quantile regression and multiple imputation combined to interpolation those censored data. A new method will eventually have to The results with the results of other methods have made some appropriate comparison, found using this method results in line with expectations. The purpose of this paper is to propose a new method to the censored data included in and fix it, so as to improve the estimation efficiency. The main structure is as follows: the first chapter is the introduction, it mainly introduces the research background, significance, literature review, and inform the context, namely the research ideas and framework, the other is the main innovation of this study. The second chapter first introduces the basic concepts and quantile quantile regression, and then the parameter estimation method. The theory of nature and the censor quantile regression is introduced. The paper finally points out some theoretical basis of multiple imputation method. The third chapter focuses on the response variables are censored data interpolation The introduction of a new method based on multiple imputation method of quantile regression technique, first introduced the basic theory related to it, and then use the method of multiple fixed censored case is simulated, and a detailed analysis of the simulation results. In the fourth chapter, the proposed method was applied to actual data the example and make the appropriate analysis of the results. The fifth chapter is the summary of the proposed method, and put forward the limitations of this paper.

【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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