拟似然方法在广义半函数部分线性模型中的应用

发布时间：2018-01-27 02:15

  本文关键词： 拟似然 函数型变量 广义半函数部分线性模型　出处：《云南大学》2016年硕士论文　论文类型：学位论文

【摘要】：随着社会的发展,计算机存储能力和处理速度的提升,我们在环境科学、化学、生物学、医学、经济学等越来越多的领域观测到的数据越来越精细。例如,对一个现象我们可以观测一个大样本的变量,进一步我们来看一个通常的情形：某个随机变量可以在范围(t min,tmax)的一些时间点上取值,则它的一个观测样本可以通过随机族{X(tj)} j=1,....,J来表示。在现代统计中,给定范围时的观测数据越来越多意味着连续不断的常数越来越靠近。传统统计方法和统计模型在处理这类数据时存在很多问题,如过拟合和维数祸根问题。为解决这些困难,统计学者们把这些观测到的大样本数据考虑成连续族,将每个个体看成一条曲线,从而对曲线数据进行统计分析。这就是本文中函数型数据的基本思想。部分线性模型理论首先由Engle et al(1986)提出,随后被广泛研究和应用在应用统计的许多领域。这种模型允许一部分解释变量为参数形式,而另一部分解释变量为非参形式。随后Thomas把此模型推广到广义形式。本文应用拟似然方法来对广义部分线性模型进行估计,并利用近年来函数型数据在非参数统计方面的发展,把函数型数据引入到解释变量的估计中来,研究广义半函数部分线性模型,对模型中参数估计量的一些渐进性质进行了说明。最后,用一个实值例子来说明本文中模型的估计效果。
[Abstract]:With the development of society and the improvement of computer storage capacity and processing speed, we have observed more and more fine data in more and more fields such as environmental science, chemistry, biology, medicine, economics and so on. For example. For a phenomenon we can look at a large sample of variables, and further, let's look at the usual situation: a random variable can be selected at some point in time in the range of mint / t _ max. (_ _ _). Then one of its observation samples can be represented by the random family {Xtj)} JJ. The increasing number of observed data in a given range means that the constant is getting closer and closer. Traditional statistical methods and statistical models have many problems in dealing with such data. In order to solve these difficulties, statisticians consider these large sample data as a continuous family and treat each individual as a curve. This is the basic idea of the functional data in this paper. The partial linear model theory was first put forward by Engle et alin1986). It has been widely studied and applied in many fields of applied statistics. This model allows some explanatory variables to be parameterized. Then Thomas extended the model to the generalized form. In this paper, the quasi-likelihood method is used to estimate the generalized partial linear model. Based on the development of nonparametric statistics of functional data in recent years, this paper introduces the functional data into the estimation of explanatory variables, and studies the generalized semi-functional partial linear model. Some asymptotic properties of the parameter estimator in the model are explained. Finally, a real value example is used to illustrate the estimation effect of the model in this paper.
【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1
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本文编号：1467274