缺失数据下广义非线性回归模型基于经验似然的统计诊断

发布时间：2018-05-23 07:10

本文选题：广义非线性回归 + 缺失数据　；参考：《南京理工大学》2017年硕士论文

【摘要】：论文研究的是带有缺失数据的广义非线性模型基于经验似然的统计诊断,对非线性模型进行了推广,首先利用经验似然的方法来对参数进行估计,并构造了参数的渐进置信区间。当响应变量随机缺失时,取缺失概率分别为π(x)=0.5,0.8,样本容量分别为n=20,50,100,每种情况重复模拟2000次,通过模拟,得出结论:经验似然方法的覆盖率与一般方法的覆盖率相比都比较大;对于固定的缺失概率π,随着样本容量n增大,经验似然方法与一般方法的平均区间长度均变短,覆盖率均增加。当样本容量n固定,缺失概率π越大,经验似然方法与一般方法的覆盖率越大,平均区间长度越短,但是经验似然方法比一般方法更加明显的提高了覆盖率。接着又对模型进行统计诊断,介绍了如何检测实际数据与既定模型之间可能存在的偏离,对模型进行数据删除度量和局部影响分析,并提出经验似然距离、经验Cook距离以及标准化残差等诊断统计量。最后又结合实例进行分析,选择合适的模型,找出了数据中的强影响点,验证了诊断统计量的有效性。
[Abstract]:In this paper, the generalized nonlinear model with missing data is studied based on the statistical diagnosis of empirical likelihood, and the nonlinear model is generalized. First, the parameters are estimated by the empirical likelihood method. The asymptotic confidence interval of the parameters is constructed. When the response variables are randomly missing, the probability of deletion is 0. 50.8, the sample size is nong 2050100, and the simulation is repeated 2000 times in each case. Through simulation, it is concluded that the coverage of the empirical likelihood method is larger than that of the general method. For the fixed loss probability 蟺, with the increase of sample size n, the average interval length of both the empirical likelihood method and the general method becomes shorter and the coverage rate increases. When the sample size n is fixed, the loss probability 蟺 is larger, the coverage of empirical likelihood method and general method is larger, and the average interval length is shorter, but the empirical likelihood method increases the coverage rate more obviously than the general method. Then it makes statistical diagnosis of the model, introduces how to detect the possible deviation between the actual data and the established model, measures data deletion and local impact analysis of the model, and puts forward the empirical likelihood distance. Empirical Cook distance and standardized residuals and other diagnostic statistics. Finally, an example is used to analyze and select the appropriate model to find out the strong influence points in the data, and verify the validity of the diagnostic statistics.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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