线性混合效应模型的正态性检验

发布时间：2018-11-16 14:04

【摘要】：纵向数据经常出现在生物,经济,气象,工业等领域,在研究连续性纵向数据时普通的线性回归模型显然不能很好的解释数据,人们通常采用带有随机效应项的混合效应模型来进行数据建模.我们往往假设模型中随机误差项与随机效应项是服从正态分布的,在此基础上使用极大似然估计(MLE)和限制极大似然估计(RMLE)等方法可以很方便地研究参数性质,并且得到很好的结论.然而实际数据中很难满足正态性假设,如果在构建数据模型时不顾正态性假设的条件要求而强行建模,往往会得到错误的结论.因此本文主要研究线性混合效应模型中随机误差项的正态性检验以及固定效应的参数估计问题.由于随机误差是不可观测的,所以在进行正态性检验之前需要对随机误差进行估计,这就需要估计随机效应和固定效应.本文首先使用QR分解的方法将随机效应项移除,在此基础上采用SCAD (Smoothly clipped absoluted deviation)方法对模型的固定效应进行变量选择与估计,理论研究表明SCAD方法得到的估计量在满足一定的假设条件下是√n-相合的.其次本文将BHEP(Baringhaus-Henze-Epps-Pulley)多维正态性检验方法进行了推广,针对随机误差的估计构造检验正态分布的检验统计量.研究发现本文根据BHEP方法构造的检验统计量在原假设成立的情况下渐近收敛于一个零均值的高斯过程,并且通过模拟研究验证本文提出方法的有效性.
[Abstract]:Longitudinal data often appear in the biological, economic, meteorological, industrial and other fields. In the study of continuous longitudinal data, the ordinary linear regression model obviously can not explain the data very well. People usually use mixed effect model with random effect term to model data. We often assume that the random error terms and the random effect terms in the model are normally distributed. On this basis, we can easily study the properties of the parameters by using the methods of maximum likelihood estimation (MLE) and restricted maximum likelihood estimation (RMLE). And come to a good conclusion. However, it is difficult to satisfy the normal hypothesis in the actual data. If the data model is constructed regardless of the conditional requirements of the normality assumption, the wrong conclusion will be obtained. In this paper, we mainly study the normality test of random errors and the parameter estimation of fixed effects in the linear mixed effect model. Because the random error is not observable, it is necessary to estimate the random error before the normality test, which requires the estimation of the random effect and the fixed effect. In this paper, the random effect term is removed by QR decomposition method, and then the fixed effect of the model is selected and estimated by SCAD (Smoothly clipped absoluted deviation) method. Theoretical studies show that the estimators obtained by the SCAD method are square n- consistent under certain assumptions. Secondly, the BHEP (Baringhaus-Henze-Epps-Pulley) multidimensional normality test method is extended to construct test statistics for the estimation of random errors. It is found that the test statistics constructed in this paper according to the BHEP method converge to a Gao Si process with zero mean asymptotically under the original hypothesis, and the effectiveness of the proposed method is verified by simulation studies.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1

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