【作者】 袁权龙；

【导师】 喻胜华；

【作者基本信息】 湖南大学 ， 概率论与数理统计， 2005， 硕士

【摘要】 线性模型是一类很重要的统计模型,它包括回归模型、方差分析模型、协方差分析模型以及混合模型等。这一模型在许多领域如生物、医学、工业、农业、工程学、经济、管理等方面都有广泛而重要的应用。同时,线性模型的基本理论与方法也为其它统计理论与方法提供了基本的工具。特别地,多元线性模型和一般生长曲线模型是线性模型中两类重要的模型。 模型的预测问题就是利用已知观察值去预测未知观察值。本文研究了线性等式约束下一般生长曲线模型中条件可预测变量的最优预测,并证明了它在几乎处处意义下的唯一性,以及在不同可预测变量下一般生长曲线模型的简单投影预测。此外,还研究了线性模型最优线性无偏预测的稳健性。本文研究了任意秩多元线性模型中最优线性无偏预测的稳健性问题,得到了线性可预测变量的这种预测关于协方差矩阵具有稳健性的充要条件,并将这方面的结果推广到了线性等式约束下的多元线性模型、一般生长曲线模型及线性等式约束下的一般生长曲线模型。最后,我们还研究了一般生长曲线模型在不同可预测变量下的简单投影预测关于协方差阵的稳健性。更多还原

【Abstract】 Linear model is a vital class of statistical model which involves regression model、 variance analysis model、 covariance analysis model and mixed model etc. It is widely applied in biology、 medicine、 industry、 agriculture、 engineering、 economics、 administration etc. Morever, linear model’s basic theory and methods are basic tools of other statistical ones. Specially, multivariate linear model and the general curve model are two classes important model of linear model.The prediction problem is to predict the unknown observation by using the known ones. In this paper, the conditional optimal prediction of the conditional predictable variable in the general growth curve model and linear equality constraints is investigated, which is unique with probability one, are obtained. And the simple projection predictor in the general growth curve model with different linear predictable variable is investigated. In addition, robustness of linear model optimal prediction are investigated. Robustness of the best linear unbiased prediction in the multivariate linear model with arbitrary bank are investigated. Necessary and sufficient conditions for the predictor of linear predictable variable to be robust with respect to covariance matrices are obtained, thus extending the results of robustness to the multivariate linear model with arbitrary bank and linear equality constraints、 the general growth curve model、 the general growth curve model with linear equality constraints. Finally, robustness of the simple projection predictor in the general growth curve model with different linear predictable variable on the covariance matrix are investigated.更多还原