论文标题:含随机效应的增长曲线模型回归参数阵的估计
The Estimates of Regression Coefficient Matrix in the Growth Curve Model with Random Effects
论文作者 罗幼喜
论文导师 刘贤龙,论文学位 硕士,论文专业 概率论与数理统计
论文单位 华中师范大学,点击次数 116,论文页数 33页File Size912k
2005-05-01论文网 http://www.lw23.com/lunwen_267718087/ 增长曲线模型;随机效应;回归系数阵;最小二乘估计; 极大似然估计; 最佳线性无偏估计;两步估计
growth curve model; random effects; regression coefficient matrix; LSE; MLE; BLUE; two-stage estimate
文章考虑了增长曲线模型: 和含随机效应的增长曲线模型: 全文共分三章,第一章介绍了此模型的由来及相关的研究成果。第二章首先简单介绍了回归参数阵(?)的三种常见估计:MLE,LSE,BLUE,然后着重讨论了MLE,BLUE与LSE相等的条件。第三章讨论了可估函数K(?)L的两步估计问题,主要包含两个方面:一方面是两步估计的计算问题,二是两步估计的优良性。文章首先给出了一个较为简便的计算两步估计的方法,然后得到了可估函数两步估计具有无偏性的一个基本结论,利用该结论文章证明了两种常见两步估计均具有无偏性。
We considers The Growth Curve Modeland The Growth Curve Model with Random Effects:The paper is organized into three chapters.Firstly the relative backgrounds of the two models and their recent research results are introduced in chapter 1. In chapter 2,we firstly introduced three familiar estimates of regression coefficient θ : MLE, LSE, BLUE ,then discussed under which condition the BLUE or MLE is identical to the LSE. Chapter 3 is devoted to discuss the two-stage estimate of KθL,which mainly included two sides: one side is how to compute the two-stage estimate; the other is about its optimal properties .Firstly we give a rather easy method of computing the two-stage estimate, then give a fundamental conclusion on how it was become an unbiased estimate,using this conclusion we proofed two important two-stage estimates are unbiased estimates.
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