自助法在极大似然估计稳健性中的应用
毕业论文关键词：自助法 线性模型 极大似然估计 稳健性
Bootstrap robustness in maximum likelihood estimation
ABSTRACT
This paper studies the bootstrap method of maximum likelihood estimation robust applications , the first bootstrap method is an important method of statistical inference statistics in assessing and improving the accuracy of self- Efron made so far, its theoretical system has been in continuous development and improvement . scholars and self- study method widely applied to practical problems in various fields , such as financial , medical , military , foreign trade , biomedical and so on. Maximum likelihood estimation is an estimation method. It was first proposed by Gauss. Later, in 1912 for the Fisher article reintroduced , and prove some properties of this approach. Its research is also quite mature , have better statistical properties , such as the linear model parameters with the line , non- bias, validity , and so on . However, a statistical method not only requires a good sense of general nature , and should have the robustness of the model which is designed to ensure a reasonable outcome and effectiveness of an important role. Robustness is the nature of the statistical methods stability on statistical models . This paper describes the bootstrap method of maximum likelihood estimation robustness of applications , first introduced in this research, research status at home and abroad , the principle of bootstrap method of maximum likelihood estimation and the robustness of the application to make the
system understand and comment .
Keywords: Bootstrap Linear Model The Maximum Likelihood Estimation Robustness
引 言
自助法是统计推论中评估和改善统计量精度的一种重要的方法。它是继刀切法之后的又一种再抽样的方法。自Efron首次提出至今，其理论体系一直在不断发展和完善，基本已经形成一套完整的理论体系，许多学者将自助法广泛的应用于各个领域，如金融、医学、军事、外贸、生物医学等。本文研究其在极大似然估计稳健性的应用。就是对一个线性模型的参数给出极大似然估计和稳健性统计量，用自助法对其做出评估。
文献【1】给出了自助法的定义及其性质和简单的应用，文献【2】、【3】则介绍了一般多元线性模型下，满足一般假定的条件下参数估计量的极大似然估计，本文根据这些假设给出关于随机误差项 的假设，进而得到参数的估计量及其性质，文献【7】、【8】、【9】则给出了构造稳健性统计量的内容，本文根据构造稳健性统计量的方法做出用参数的极大似然估计量构造稳健性统计量，类似的推导出它们的一些性质。
本文将对这些稳健性统计量进行研究，利用软件产生随机数据对其进行模拟，进而对稳健性统计量的性质进行评估。
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