【作者】 施露芳；

【导师】 刘次华；

【作者基本信息】 华中科技大学 ， 概率论与数理统计， 2006， 硕士

【摘要】 污染数据是生物统计和金融统计中常见的一类数据,它也是一类不完全数据.由于试验设计、设备误差、条件限制以及观测者主观因素等原因,我们得到的是不完全数据.不完全数据并不是完全不能利用的数据,虽然有时可以再做一次数据的统计工作,但大多数时候是不可重复、费时太长或是代价太高的.而且,在固定的污染源未查明或被消除的情况下,只可能得到被污染的数据.因此,关于污染数据的统计分析已发展成为统计推断一个重要专题.本文重点研究了带污染数据的回归模型参数估计问题.第一章简要介绍了选题的背景,包括“回归”的特点、发展,污染数据的产生背景以及国内外研究状况.第二章介绍了截断情形下带污染数据的模型参数估计,包括截断模型下的污染系数的估计,有两种方法:一种是基于截断数据的均值估计的想法,得到了污染系数的估计,且估计具有渐近正态性,另一种是利用研究截断数据回归分析的想法来做,同样得到了具有良好性质的估计;接着使用矩估计法得到了截断的污染数据的参数估计;最后利用最小二乘法及矩估计方法得到了截断情形下污染数据半参数回归模型的参数估计.第三章介绍了污染数据线性回归模型的估计问题.首先介绍了一些基础知识,然后重点介绍了我所做的工作:讨论简单回归模型中响应变量受到另一随机变量序列污染时,模型参数和污染系数的估计方法.利用贝叶斯统计原理,给出了污染系数的后验置信区间及模型参数估计.由于引入先验信息,增加了被估参数的信息,它对于提高估计的性能是有益的.在实际中,有广泛的应用价值.第四章介绍了污染数据半参数回归模型的估计方法.首先利用矩方法给出了两种污染方式下污染参数及污染系数的估计.然后介绍了我所做的另一工作:利用(线性)小波估计方法,给出了未知待估参数β,未知函数g (? )以及污染参数υ的估计,并证明了它们的弱相合性.小波方法用于回归模型,在对待估函数要求较低的情况下,得到了比较优良的性质.第五章是总结和展望.更多还原

【Abstract】 Contamination data is a common statistical data in Biological Statistics and Financial Statistics, it is also a incomplete data .There are much factors such as experimental design ,equipment error, restrictions and observers subjective factors,so we are given incomplete data. However, the use of incomplete data is not entirely.Although sometimes we can do a statistical data, but most of the time it is cannot be duplicated, time-consuming too long or the price too is high.Moreover, in the situation which the stationary source has not verified or eliminated,we only obtain the contaminated data.Therefore, the statistical analysis of contamination data have become an important topic. This paper importantly studies the estimation of parameter in regression model which contains contamination data.In chapter one,the problem’s background is introduced,including the characteristics and development of regression,the background of contamination data and research at home and abroad.In chapter two,it introduces the estimation of parameter in regression model which contains contamination data under the situation of censord data,including the estimation of contamination coefficients of censord data:one is based on the mean estimate of censord data ,the other is to use the idea to do research on the analysis of regression with censord data;the use of moment estimation method in parametric estimation of broken contamination data;estimation method of semiparametric regression model with contaminated and censord data,and this paper presents the estimations of model parametric and contamination parametric respectively by using least-squares method and moment estimation method.In chaper three,it introduces the estimation method of linear regression model with contaminated data.First,much basic knowledge is introduced.Then,it importantly introduces my perspective : in this paper the estimations of the parameters and coefficient of contamination for the simple regression model and studied when its response variables are contaminated by another random variable sequence it discusses that the interval estimation of posterior confidence probability of parameters on coefficient of contamination by using the method of Bayes inference. And it gives the point estimation of the parameters in the model.As a result of the introduction of priori,it increased the information of estimated parameter, which is useful for improving the performance of the estimates. Application of this method have been a lot of attention to other area.In chaper four, it introduces the estimation method of semiparametric regression model with contaminated data.First , it presents the estimations of model parametric and contamination parametric respectively by using moment estimation method. Then, it importantly introduces my another perspective:we apply (linear) wavelet estimation method to model and give the definition of the unknown parameters to be estimatedβ, unknown function g (? ) and contaminated parameterυ, then prove their weak consistency.When wavelet method is used in regression model, the treatment of conditions that require lower , good nature will be succeed.In last chaper,there are summary and outlook.更多还原