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Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models

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science china.Mathematics 2004年第6期47卷 882-893页

作者： YUE Li & chen xiru school of Mathematics and Statistics, Wuhan university, Wuhan 430072, china.graduate school, Chinese Academy of sciences, beijing 100039, china 1. school of Mathematics and Statistics Wuhan University 430072 Wuhan China 2. graduate school Chinese Academy of Sciences 100039 Beijing China

Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.

关键词： quasi-likelihood function generalized linear models strong consistency

Adaptive quasi-likelihood estimate in generalized linear models

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science china.Mathematics 2005年第6期48卷 829-846页

作者： chen Xia & chen xiru school of Mathematics and Statistics, Wuhan university, Wuhan 430072, china.graduate school, Chinese Academy of science, beijing 100049, china 1. school of Mathematics and Statistics Wuhan University 430072 Wuhan China 2. graduate school Chinese Academy of Science 100049 Beijing China

This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.

关键词： generalized linear models, quasi likelihood estimate, adaptive estimate.

Existence of unbiased estimate of regression parameters in simple linear EV models

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science china.Mathematics 2005年第7期48卷 915-928页

作者： LIU Jixue & chen xiru Department of Statistics and Finance, university of science and technology of china, Hefei 230026, china.Department of Mathematics, graduate school of Chinese Academy of sciences, beijing 100049, china Department of Statistics and Finance University of Science and Technology of China Hefei 230026 China Department of Mathematics Graduate School Chinese Academy of Sciences Beijing 100049 China

It is well known that for one-dimensional normal EV regression model X = x+ u,Y =α+βx+e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and β are not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and β under some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of a and β exist, and the form of the MVUE of a and β are also given.

关键词： EV regression model unbiased estimate identiflability.

Linear EV model with replicate observations on independent variables

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science china.Mathematics 2006年第6期49卷 752-769页

作者： LIU Jixue, ZHANG Sanguo & chen xiru Department of Statistics and Finance, university of science and technology of china, Hefei 230026, china.Department of Mathematics, graduate school of Chinese Academy of sciences, beijing 100049, china 1. Department of Statistics and Finance University of Science and Technology of China Hefei 230026 China 2. Department of Mathematics Graduate School of Chinese Academy of Sciences Beijing 100049 China

This paper studies the linear EV model when replicate observations are made only on independent variables. We construct the estimates of regression coefficients and prove the consistency and asymptotic normality under some proper conditions. Results obtained reveal the difference between the case where the independent and dependent variables are observed repeatedly and simultaneously and the case studied in this article.

关键词： linear EV model, consistency, asymptotic normality.

EXISTENCE OF CONSISTENT ESTIMATES OF LINEAR REGRESSION COEFFICIENTS WHEN THE ERROR VARIANCES ARE UNEQUAL

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Systems science and Mathematical sciences 1992年第3期5卷 251-259页

作者： JIN Mingzhong (Institute of Systems science,Academia Sinica,beijing 100080,china.chen xiru (graduate school,university of science and technology of china.beijing 100239,china.

Consider the linear regression model Yi=xi′β+σiei,i=1,…,n,…,where E（ei）=0,E（eiej）=δij,012（?）σ22（?）…and {xi} satisfies A1（?）sum from i=1 to n xixi′/n（?）A2,for n large,A1>0,A2>*** paper shows that （i） ifσi2,i=1,2…,are known,then the necessary and sufficient condition for theconsistency of the best unbiased linear estimate of β is sum from i=1 to ∞σi-2=∞;（ii）if{σi2}is only known to belong to the set {（h1,h2,…）∶01（?）h2（?）…,sum from i=1 to ∞ hi-1=∞},then no mean-square consistent linear estimate of β exists,and,if e1,e2,…are independent and satisfy a minor condition,then no weakly consistent linearestimate of β *** related open problems are suggested.

关键词： Linear regression model consistency

STRONG CONSISTENCY OF M-ESTIMATES OF MULTIPLE REGRESSION COEFFICIENTS

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Systems science and Mathematical sciences 1995年第1期8卷 82-87页

作者： chen xiru (graduate school of the Chinese Academy of sciences, beijing 100039, china.ZHAO Lincheng (Department of Mathematics, university of science and technology of china, Hefei 230026, china.

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关键词： Linear regression M-estimate strong consistency.

A Necessary Condition for the Consistency of LAD Estimate

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Acta Mathematica Sinica,English Series 1996年第3期12卷 292-297页

作者： chen xiru, Department of Mathematics graduate school, Academia Sinica beijing 100039, china.u Yuehua, Department of Mathematics York university, TorontoZhao Lincheng, Department of Mathematics university of science and technology of china Heifei 230026, china Academia Sinica York university university of science and technology of china

If in the linear model （1）the random errors e1, e2,...satisfy assumption （B）（See Section 1）, then a necessary condition for the consistency of the LAD estimate of βo is sum from i=1 to∞‖xi‖2=∞.

关键词： Linear model LAD estimates Consistency

CONSISTENCY OF LS ESTIMATOR IN SIMPLE LINEAR EV REGRESSION MODELS

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Acta Mathematica Scientia 2005年第1期25卷 50-58页

作者：刘继学陈希孺 Department of Statistics and Finance university of science and technology of china Hefei 230026 China Department of Mathematics graduate school of Chinese Academy of sciences Beijing 100039 China

Consistency of LS estimate of simple linear EV model is studied. It is shown that under some common assumptions of the model, both weak and strong consistency of the estimate are equivalent but it is not so for quadra... 详细信息

关键词： EV model consistency

A STUDY ON THE CROSSLINK ABILITY OF DIFFERENT COMPONENTS IN COLLAGEN AND GELATIN

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中国科学院大学学报(中英文) 1997年第2期14卷 188-194页

作者： Fu Xiaomin(Biology Department,graduate school at beijing,university of science and technology of china.beijing 100039)Peng Bixian chen Lijuan(Institute of Photographic Chemistry,Academia Sinica,beijing 100101) 中国科学技术大学北京研究生院生物学部北京中科院感光化学所北京

The crosslink ability with HCH0 of different components （sub-units） in collagen and gelatin were investigated. We made a series of comparisons between the components. The difference of crosslink ability was discussed. There is no obvious difference between the crosslink ability of α βcomponents in acid soluble collagen and those of the same components in photographic gelatin. The crosslink ability of α2is greater than that of α1: but the crosslink ability of β11is similar to that of β12, and β components have obviously hydroIyzed during crosslink process. This situation happens in components of collagen as well as in components of gelatin.

关键词： collagen gelatin component crosslink CM-52 SDS-PAGE