线性混合模型中的Bootstrap方法的研究及应用

发布时间：2018-03-05 04:02

本文选题：异方差　切入点：套设计模型　出处：《北方工业大学》2014年硕士论文　论文类型：学位论文

【摘要】：统计模型中一种重要的模型就是混合效应模型,该模型可广泛应用于生物统计、经济管理、医疗案例分析等重要的前沿领域。其中混合模型中固定效应以及随机效应的显著性检验一直是统计学家研究的重点。而套设计模型作为一种特殊的混合效应模型,通常是由于社会的分级结构、数据的重复测量以及含个体效应和时间效应的经济问题等原因而产生的；其广泛应用于多层统计分析中,并在区域经济调查和计量经济学等领域也经常被用到。因此,在套设计模型中有关固定效应和随机效应的显著性检验问题也至关重要。本文主要对在异方差下两级套设计模型中的固定效应以及随机效应的显著性进行检验,并且也对异方差下一般混合效应模型中方差分量的检验问题进行了分析。本文的研究内容包括以下两个方面： 1.研究了在异方差下两级套设计模型中主效应和随机效应的存在性问题。针对主效应的检验,提出了一种PB检验方法,并将其与已存在的GF检验进行比较,用MC模拟两种检验方法犯第一类错误的概率。我们的研究表明：PB检验比GF检验更加优越。尽管在小样本模型中,GF检验、PB检验都具有令人满意的结果,但当因子组合数或者处理组的数量增加时,GF检验会有比较严重的第一类错误。我们的研究还表明：有关两级套设计模型中随机套效应的方差分量是否为零的检验,该方法同样适用。 2.对异方差下两级套设计模型的随机套效应方差分量是否小于等于某个给定的正数进行检验。利用重抽样的思想,提出了一种PB检验方法,并将其与己存在的GF检验进行比较,用MC方法模拟两个检验方法犯第一类错误的概率。研究表明：此时PB检验有比较好的检验效果。本文还对一般混合效应模型中的设计矩阵进行谱分解,在此基础上,给出一种PB检验方法,并利用MC方法模拟其犯第一类错误的概率。
[Abstract]:One of the most important models in statistical models is the mixed effect model, which can be widely used in biological statistics, economic management, Medical case analysis and other important frontier fields. Among them, the significance test of fixed effect and random effect in mixed model has been the focus of statisticians. As a special mixed effect model, the set design model is a special hybrid effect model. It is usually caused by the hierarchical structure of society, repeated measurements of data, and economic problems with individual and time effects; it is widely used in multilayer statistical analysis. And is often used in areas such as regional economic surveys and econometrics. It is also very important to test the significance of fixed effect and random effect in jacket design model. This paper mainly tests the significance of fixed effect and random effect in two-stage jacket design model under heteroscedasticity. The test problem of variance component in general mixed effect model under heteroscedasticity is also analyzed. The research content of this paper includes the following two aspects:. 1. The existence of main effect and random effect in two-stage jacket design model under heteroscedasticity is studied. A PB test method is proposed for the test of principal effect and compared with the existing GF test. Using MC to simulate the probability of making the first error in two test methods. Our study shows that the w PB test is superior to the GF test. However, when the number of factor combinations or the number of treatment groups increases, there will be serious errors in the first class of the GF test. Our study also shows that the test of whether the variance component of the random sleeve effect in the two-stage sleeve design model is zero or not. The method is also applicable. 2. To test whether the variance component of random sleeve effect of two-stage jacket design model under heteroscedasticity is less than or equal to a given positive number, a PB test method is proposed by using the idea of re-sampling, and compared with the existing GF test. MC method is used to simulate the probability of two test methods making the first kind of error. The results show that PB test has better test effect at this time. In this paper, the design matrix in general mixed effect model is decomposed by spectrum, and on this basis, In this paper, a PB test method is presented, and the probability of making the first kind of mistake is simulated by MC method.
【学位授予单位】：北方工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O212.1

【参考文献】