不可忽略缺失数据下非线性模型的经验似然推断

发布时间：2018-01-23 13:44

本文关键词： 经验似然逆概率加权非线性模型置信区域不可忽略缺失数据　出处：《云南大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文成功地将经验似然方法应用到带有不可忽略响应变量缺失的非线性模型。所有的目标参数的经验似然估计量或者经验似然函数将通过两步获得。第一步,假设缺失机制是一个参数Logistic回归模型后,应用极大似然估计方法可以得到缺失概率(倾向得分函数)的一个相合估计。一旦获得缺失概率的相合估计,基于指数倾斜模型,本文获得三个渐进无偏的估计方程,这也是下文的运用经验似然方法的核心思想。特别的,三个无偏估计方程的定义分别基于逆概率加权、非参插补、增强逆概率加权。第二步,将计算所有的目标参数的经验似然估计量或者经验似然函数。基于第一步构建的无偏估计方程,建立了获得回归系数的经验似然置信区间或者置信域的理论和方法,且研究了所提出的经验似然比统计量的极限分布的理论性质。同时,本文获得了目标参数的经验似然估计量且还研究了该估计量渐进分布的性质。在我们实际的研究当中,有关于协变量的辅助信息可以使用。为此,本文还提出了基于辅助信息的目标参数的两步更有效的经验似然估计量。在使用辅助信息以后,目标参数的经验似然估计量或者经验似然函数也将通过两步获得,唯一的区别在于使用辅助信息可以获得更好而且更有效的估计。另外,在获得参数化的缺失概率(倾向得分函数)的相合估计后,本文提出的基于辅助信息的经验似然方法可以很好地解决估计方程中参数个数小于估计方程个数的问题。更重要的是参数化的倾向得分函数估计比半参数的核实样本估计方法要更稳定更好。本文还系统地研究了在辅助信息使用以后所提出的经验似然估计量的大样本性质。最后,用两个数值模拟研究和一个实例分析来说明所提出的理论在有限样本下具有较好的表现。
[Abstract]:In this paper, the empirical likelihood method is successfully applied to the nonlinear model with the absence of non-negligible response variables. The empirical likelihood estimators or empirical likelihood functions of all the target parameters will be obtained in two steps. It is assumed that the missing mechanism is a parameter Logistic regression model. A consistent estimation of the loss probability (tendency score function) can be obtained by using the maximum likelihood estimation method. Once the consistent estimation of the loss probability is obtained, the exponential tilt model is used. In this paper, we obtain three asymptotic and unbiased estimation equations, which is the core idea of empirical likelihood method. In particular, the definitions of the three unbiased estimation equations are based on inverse probabilistic weighting and non-parametric interpolation respectively. The second step is to calculate the empirical likelihood estimator or empirical likelihood function of all the target parameters. The unbiased estimation equation based on the first step is constructed. The theory and method of empirical likelihood confidence interval or confidence region for obtaining regression coefficients are established, and the theoretical properties of the limit distribution of empirical likelihood ratio statistics are studied. In this paper, the empirical likelihood estimator of target parameters is obtained and the properties of the asymptotic distribution of the estimator are also studied. In our actual study, there are auxiliary information about covariables that can be used. This paper also proposes a two-step empirical likelihood estimator for object parameters based on auxiliary information. The empirical likelihood estimator or empirical likelihood function of the target parameter will also be obtained in two steps. The only difference is that the auxiliary information can be used to obtain better and more effective estimation. After obtaining the consistent estimation of the parameterized absence probability (tendency score function). The empirical likelihood method based on auxiliary information proposed in this paper can solve the problem that the number of parameters in the estimation equation is smaller than the number of estimated equations. More importantly, the parameterized tendency score function estimation is better than the verification of semi-parameter. The sample estimation method is more stable and better. This paper also systematically studies the large sample properties of the empirical likelihood estimator proposed after the auxiliary information is used. Two numerical simulation studies and an example analysis are used to show that the proposed theory has a good performance in finite samples.
【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1

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