广义线性模型论文广义线性模型中极大拟似然估计的相合性与渐近正态性.docVIP

广义线性模型论文：广义线性模型中极大拟似然估计的相合性与渐近正态性【中文摘要】广义线性模型是一类非常重要的数学模型,是经典线性模型的推广,有着广泛的应运。在经济,社会,医学,生物等数据的统计分析上有这重要的意义。可以适用于连续数据与离散数据,尤其是后者,如计数数据,属性数据等等。广义线性模型包括线性回归,方差分析模型,交替响应的对数和概率单位模型模型,对数线性模型,计数的多项响应模型和生存数据的一些常用模型。以上这些模型具有大量的性质,例如线性性,我们可以使用这些性质得到很好的效果。除此之外,我们还有计算参数估计的常用方法。广义线性模型的个例起源很早,世界著名统计学家费舍尔曾于1919年使用过该模型。1972年Nelder和Wedderburn在一篇论文中引进了广义线性模型的概念。1989年McCullagh和Nelder再版的著作详细的论述了广义线性模型及其取得的成果。时至今日,这方面的研究文献数以千计。本文研究了广义线性模型的参数估计,研究估计的渐近性,包括渐近存在性,相合性和渐近正态性。1.本文研究了在自适应设计和自联系情况下,广义线性模型极大拟似然的渐近存在性。当响应变量yi是q1维,设计阵Xi是pq维且有界,以及最小特征根sup E以及其它正则条件下,证明了极大拟似然估计(MQLE)的渐近存在性,弱相合性和收敛速度。之前没有文献在n的条件下,获得相应的结果。2.本文研究了在自适应设计和自联系情况下,广义线性模型极大拟似然的渐近正态性性。当响应变量yi是q1维,设计阵Xi是pq维且有界,及及其它的正则条件下,广义线性模型有一个渐近正态的根。这将高启兵和吴耀华(2004)中的条件减弱到了【英文摘要】The generalized linear model, which is the classical linear model promotion, is a kind of very important mathematical model and has been widely used. It is very significant in data analysis in the economy, the society, the medicine, in biology and so on. It is suitable for the continuous and the discrete data, particularly the latter, like counted data, characteristic data and so on. The generalized linear model includes models such as the peculiar circumstance, the linear regression, the variance analysis model, the logarithm and the probit model of alternated responds, the log-linear model, the counting many response model and some commonly used models of survival data. There are massive properties in some models above, such as the linearity. We can use these properties to obtain the very good effect. In addition, we also have commonly used methods of the parameter estimation.Generalized linear models example originated very early. World-famous statistician Fish once used this model in 1919. In 1972 Nelder and Wedderburn introduced the concept of the generalized linear model in a paper. In 1989 McCullagh and Nelder discussed the generalized linear model and obtained achievement in their reprinted work in detail. Now there is much literature in this aspect.In this paper, parameter estimation of the generalized linear model is studied. The asymptotic properties of parameter estimation are discussed, including consistency, asymptotic existence and normality.1. The consistency of maximum quasi-likelihood estimators (MQLEs) in generalized linear models with natural link function and adaptive designs is discussed. When the response yi is q x 1 dimensional random vectors, the p x q regressors Xi is bounded, the minimum eigenvalue sup E and the other mild conditions, the consistency, asymptotic existence and the rate of MQLEs are proved. Corresponding results are not obtained until now when2. The asymptotic normality of maximum quasi-likelihood estimators (MQLEs) in generalized linear models with natural link function and adaptive designs is discussed. When the response yi is q x 1 dimensional random vectors, the p x q regressors Xi is bounded, and the other mild conditions, the asymptotic normality of MQLEs is proved. This weakened in Gao Q B and Wu Y H (2004).【关键词】广义线性模型 极大拟似然估计 相合性 渐近正态性【英文关键词】generalized linear models maximum quasi-likelihood estimators consistency asymptotic normality【目录】广义线性模型中极大拟似然估计的相合性与渐近正态性摘要3-4Abstract4第一章 绪论6-161.1 广义线性模型简介6-91.1.1 线性模型简介6-71.1.2 广义线性模型简介7-91.2 极大拟似然估计理论9-121.2.1 极大似然估计理论简介9-111.2.2 极大拟似然估计理论简介11-121.3 国内外的研究成果12-141.4 本文内容安排14-16第二章 广义线性模型的渐近存在性和相合性16-262.1 引言16-192.2 主要定理和相关结果19