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	On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models
	Zhang SanGuo; Liao Yuan
刊名	Science in china series a-mathematics
	2008-07-01
卷号	51期号:7页码:1287-1296
关键词	Generalized linear models (glms) Quasi-maximum likelihood estimates (qmle) Weak consistency Convergence rate
ISSN号	1006-9283
DOI	10.1007/s11425-007-0172-7
通讯作者	Zhang sanguo(sgzhang@gucas.ac.cn)
英文摘要	In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (qmle) concerning the quasi-likelihood equationn sigma(n)(i=1) x(i)(y(i) - mu(x(i)'beta)) = 0 for univariate generalized linear model e(y vertical bar x) = mu(x(i)'beta). given uncorrelated residuals {e(i) = y(i)-mu(x(i)'beta(0)), 1 <= i <= n} and other conditions, we prove that (beta) over cap (n) - beta(0) = o(p)((gimel) under bar (-1/2)(n) n) holds, where (beta) over cap (n) (beta) over cap (n) is a root of the above equation, beta(0) is the true value of parameter beta and (gimel) under bar (n) denotes the smallest eigenvalue of the matrix s(n) = sigma(n)(i= 1) x(i)x(i)'. i. we also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. moreover, paralleling to the elegant result of drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of qmle is s(n)(-1) -> 0, as the sample size n -> infinity.
WOS关键词	LONGITUDINAL DATA-ANALYSIS ; OVERDISPERSION ; REGRESSION
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
语种	英语
出版者	SCIENCE PRESS
WOS记录号	WOS:000256964700011
内容类型	期刊论文
URI标识	http://www.corc.org.cn/handle/1471x/2384834
专题	中国科学院大学
通讯作者	Zhang SanGuo
作者单位	Chinese Acad Sci, Grad Univ, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Zhang SanGuo,Liao Yuan. On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models[J]. Science in china series a-mathematics,2008,51(7):1287-1296.
APA	Zhang SanGuo,&Liao Yuan.(2008).On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models.Science in china series a-mathematics,51(7),1287-1296.
MLA	Zhang SanGuo,et al."On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models".Science in china series a-mathematics 51.7(2008):1287-1296.

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