面板数据回归样条线混合效应模型的应用

发布时间：2018-01-03 18:43

本文关键词：面板数据回归样条线混合效应模型的应用　出处：《湖北工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：在医学、生物学、计量经济学、金融学以及农业等领域的研究中,通常会遇到面板数据。在对面板数据进行统计建模时,学者们提出了面板数据的非参数回归模型。它是面板数据模型中非常重要的一种统计模型。在解决实际问题时,面板数据非参数模型更接近真实模型,更能充分利用数据中所提供的信息。回归样条线混合效应模型,是众多面板数据非参数模型中可操作性最强,应用最为广泛的一种模型。全文共分为五章。第一章是绪论部分,阐述了面板数据的非参数回归模型的研究背景、目的以及研究意义,并介绍了面板数据混合效应模型的建模假设和模型的基本形式。第二章是理论部分,系统阐述了回归样条线混合效应(MERS)模型。包括:MERS模型的构建方法,求解模型的方法和平滑参数的确定等问题。第三章是模拟比较部分,针对回归样条线混合效应(MERS)模型与多项式方法进行蒙特卡洛模拟比较,最后得出结论:MERS模型在总体函数估计方面优于多项式方法,但在个体函数估计方面,表现不如多项式方法。另外,当预测变量与相应变量的关系未知,且两者可能存在复杂关系的情况下,MERS模型估计要比多项式方法的估计更加稳健,因而适用性更强。第四章为实证研究部分,第一个实证分析针对我国城乡收入差距与经济增长的问题,阐述了城乡收入差距的演变趋势。实证分析通过构建城乡收入差距与经济增长关系的模型,验证了我国经济增长与城乡收入差距确实存在倒U型关系。并估计了我国总体和各省个体到达峰值点的时间和峰值点的人均GDP。最后提出了缩小城乡收入差距的经济和社会政策。第二个实证分析基于MERS模型,对BMI—年龄数据集进行实证分析。得到总体均值函数的估计和总体均值函数导数的估计,通过对总体分析,估计出13.7岁为BMI增速最快的年龄;并对肥胖、超重个体的个体函数进行估计,发现肥胖和超重的触发年龄均值分别为20.41岁和21.17岁。通过分析超重、肥胖个体,发现大多数超重、肥胖个体的触发年龄在15-25周岁阶段,因此有必要在中学阶段、大学阶段,对其进行饮食、运动干预。第五章为全文总结部分。
[Abstract]:In medicine, biology, econometrics, finance, and agriculture, panel data are usually encountered. Scholars have proposed a non-parametric regression model of panel data, which is a very important statistical model in panel data model. In solving the practical problems, the non-parametric model of panel data is closer to the real model. The regression spline mixed effect model is the most operable among many panel data non-parametric models. The most widely used model. The full text is divided into five chapters. The first chapter is the introduction part, elaborated the panel data non-parametric regression model research background, purpose and research significance. And introduced the panel data mixed effect model modeling hypothesis and the basic form of the model. The second chapter is the theoretical part. The regression spline mixed effect (MERS) model is systematically expounded, including the construction method of the MERS model, the method of solving the model and the determination of smooth parameters. The third chapter is the part of simulation and comparison. Comparing the regression spline mixed effect (MERS) model with polynomial method in Monte Carlo simulation, the conclusion is drawn that the MERS model is superior to the polynomial method in the estimation of population function. But in the aspect of individual function estimation, the performance is not as good as polynomial method. In addition, when the relationship between predictive variables and corresponding variables is unknown, and there may be a complex relationship between them. The MERS model is more robust than the polynomial method, so it is more applicable. Chapter 4th is the empirical research part, the first empirical analysis is aimed at the problem of urban-rural income gap and economic growth in China. This paper expounds the evolution trend of urban-rural income gap, and establishes the model of the relationship between urban-rural income gap and economic growth. The relationship between economic growth and urban-rural income gap is proved to be inversely U-shaped, and the time of reaching the peak point and the per capita GDP at the peak point are estimated. Finally, it is proposed to reduce the income gap between urban and rural areas. The second empirical analysis is based on MERS model. Through the empirical analysis of BMI-age data set, we get the estimation of the total mean function and the derivative of the total mean function. Through the overall analysis, we estimate that the age of 13.7 years old is the fastest growing age of BMI; The average trigger age of obesity and overweight is 20.41 years old and 21.17 years old, respectively. By analyzing overweight and overweight individuals, we find that most of them are overweight. The trigger age of obese individuals is 15-25 years old, so it is necessary to carry out diet and exercise intervention in middle school and college stage. Chapter 5th is the summary of the full text.
【学位授予单位】：湖北工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F124.7

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