【作者】 刘殿国；

【导师】 夏立显；

【作者基本信息】 吉林大学 ， 地球探测与信息技术， 2005， 博士

【摘要】 本文首先综述了多层统计模型的研究现状,分析了其在应用方面的局限性,介绍了灰色系统的建模思想和模型,探讨了其应用和理论中存在的问题,并比较了线性模型与灰色系统模型预测的效果。为了克服多层统计模型和灰色系统模型各自的不足,把灰色系统的建模思想方法和多层统计模型的思想方法的精华结合起来,给出了累加方法的多层统计新模型,用数值例子验证了新模型在预测方面比原多层统计模型和灰色系统模型更有效。并对新模型的参数估计方法,残差估计方法,残差新模型,新旧数据间关系的新模型,具有周期趋势响应值的两步估计,多重共线性的克服,在异常方面的预测等问题进行了研究。最后,针对模型的背景值可以取不同值的情形,在引入了DEA方法,挖掘出DEA有效点的建模含义的基础上,给出了模型的背景值的选择方法。更多还原

【Abstract】 This text first overview the research present condition of the multilevel statistical model , analyse its limitation in the applied aspect, introduce the molding thought and method of gray system , inquire into existent problem in its applied and theories, compared the predicative result of the line model and the gray system model. combining multilevel statistical model thought, method with molding thought , method of gray systems , give multilevel statistical new model. Parameter estimate、residual estimate ,solving multicollinearity problem, Two-stage Estimate of Possession Periodical Trend data, dealing with new old data, actual Application of the new model are researched. Still aim at the model moreover to be worth the situation that can take different value in the background, in introducing the foundation of DEA method, give theories study of the background value choice method, got the choice method of the model background value. The new models progress in probing complicated data with layer structure , the choice method of the model enable people find out sooner with the actual data agrees with to match of model. Have the different characteristics in comparing multilevel staistical model with tradition statistical model : ①in data analyze, multilevel statistical model can get the more valid estimate; ②The multilevel statistical model can get to even match the actual standard error、confidence intervals and significance tests;③The passes the layer structure estimate of variance value ,can make clear the reason of the difference formation between different unit; ④When the sample of the object is few, can use the characteristics of the layer structure, see it is some one whole individual, pass to use the whole and average value and individual and a generous character for changeses, give to the individual study compare only use match the actual analysis more the sample of want the research object; ⑤Because of‘intra-level unit correlation’not the existence of zero situations, in the tradition, seeing the sample as an independent method is inapplicable. multilevel statistical model to apply this kind of situation at the right moment. As a result multilevel statistical model theories research , pressing to be explain by the simple explanatory variables、respond variables to change to many explanatory variables、many respond variables direction development; variance structure from the simple constant type to a direction of complicated function development; The method of the parameter estimate is form GLS to the more complicated estimate of method direction development that be should satisfy to certainly distribute It is in educate, the growth of the geography, child’s height, health etc. of application all obtained to compare good of result, and applied scope gradual extension. But it also has it to limitative in the applied aspect. Gray system is chase miscellaneous and disorderly original data, use accumulate method sorting to become the stronger and generating data of regulation, take generating data as the foundation to set up the mold, get the estimate value of the generting data, then the revivification becomes the original data. Put together the advantage of multilevel statistical model and gray system model, give out new multilevel statistical model AMM(1,1)、AMM(1,N ), and discussed Parameter estimate、residual estimate of the new model. The new models progress in probing complicated data with layer structure. For the new model applies in a specific way appear multicollinearity circum-stance, this text first step probe multicollinearity creating reason, this is because accumulated calculate way to increase the relativity of the data to result . The method that counteracts the ridge estimate overcome multicollinearity . For Two-stage estimate in addition to using the residual composing of variance matrix, for having the data of the period trend,first pass to compute a period ,then give an addend for correspond , the trans-formation behind of data is a mutually independent repetition data .Beg on this foundation variance estimate,beg one more estimate of coefficient. At the model new old data processing aspect, the topological that follow GM (1,1) the model rushes toward the choice, give whole data AMM (1,1), new information AMM (1,1), metabolism AMM (1,1). In the actual application of the model, aim at the situation that can appear更多还原