基于半参数回归模型参数的经验似然

发布时间：2018-03-23 05:33

本文选题：经验似然　切入点：鞅差误差　出处：《安徽工程大学》2017年硕士论文　论文类型：学位论文

【摘要】：Owen(1988)提出的经验似然(Empirical Likelihood,EL)是一个有影响力的计算密集型数据的统计方法。此方法定义了一个经验似然比函数,并使用受约束参数影响的其最大值来构建置信区间/区域。作为某种意义上分布假设自由的一种非参数似然方法,经验似然在推导未知参数的置信区间方面有许多突出的优点。例如,经验似然推理不涉及方差估计,基于经验似然的置信区域形状和方向完全由数据本身决定,等等。正因为如此,经验似然方法引起了许多统计学者的兴趣,他们将这一方法应用到各种统计模型及各种领域。本文的主要内容是研究基于半参数回归模型参数的经验似然问题。首先,我们研究在鞅差误差下高维部分线性模型参数的经验似然。在误差是相依情形,即误差是鞅差误差时,给出相应的经验似然比检验统计量,以及满足的渐近性质,并考虑模型参数的线性组合情形,然后通过一些基本条件以及一些引理证明渐近性质,并利用MATLAB数据模拟,说明经验似然方法比profile最小二乘表现效果好。其次,在鞅差误差下考虑部分函数线性模型参数的经验似然。通过Mercer's定理和Karhunen-Loeve表达式推导出部分函数线性模型的近似表达式,给出相应的经验似然比检验统计量,以及满足的渐近性质,通过一些基本条件以及一些引理证明该渐近性质。最后,我们考虑高维部分函数线性模型的经验似然。给出相应的经验似然比检验统计量,以及满足的渐近性质,通过一些基本条件以及一些引理证明该渐近性质,并利用MATLAB数据模拟,说明经验似然方法比profile最小二乘表现效果好。
[Abstract]:The empirical likelihood likelihood (ELL) is an influential statistical method for computationally intensive data, which defines an empirical likelihood ratio function. The confidence interval / region is constructed by using the maximum value affected by constrained parameters, which is a nonparametric likelihood method for the freedom of distribution assumption in a sense. Empirical likelihood has many outstanding advantages in deriving confidence intervals of unknown parameters. For example, empirical likelihood reasoning does not involve variance estimation, and the shape and direction of confidence regions based on empirical likelihood are entirely determined by the data itself. And so on. Because of this, the empirical likelihood method has attracted the interest of many statisticians, They apply this method to various statistical models and fields. The main content of this paper is to study the empirical likelihood problem based on semi-parametric regression model parameters. In this paper, we study the empirical likelihood of parameters of high dimensional partial linear model under martingale error. When the error is dependent, that is, the error is martingale difference error, the empirical likelihood ratio test statistic is given, and the asymptotic property is obtained. Considering the linear combination of the model parameters, the asymptotic properties are proved by some basic conditions and some Lemma, and the simulation results of MATLAB data show that the empirical likelihood method is better than the profile least squares representation. Secondly, The empirical likelihood of parameters of partial function linear model is considered under martingale error. The approximate expression of partial function linear model is derived by Mercer's theorem and Karhunen-Loeve expression, and the corresponding empirical likelihood ratio test statistic is given. The asymptotic property is proved by some basic conditions and some Lemma. Finally, we consider the empirical likelihood of the linear model of high dimensional partial function, and give the corresponding empirical likelihood ratio test statistic. The asymptotic property is proved by some basic conditions and some Lemma, and the simulation of MATLAB data shows that the empirical likelihood method is better than the profile least square method.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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