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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 {2. of Mathematics and Statistics, Wuhan university, Wuhan 430072. china.graduate {2., Chinese Academy of sciences, beijing 100039, china school of Mathematics and Statistics Wuhan University Wuhan China graduate school Chinese Academy of Sciences 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 {2. school of Mathematics and Statistics, Wuhan university, Wuhan 430072. china.graduate school, Chinese Academy of science, beijing 100049, china school of Mathematics and Statistics Wuhan University Wuhan China graduate school Chinese Academy of Science 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,{2., Hefei 2.002., 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,{2., Hefei 2.002., 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 China Department of Mathematics Graduate School of Chinese Academy of Sciences Beijing 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.

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 ({2. school of the Chinese Academy of sciences, beijing 100039, china.ZHAO Lincheng (Department of Mathematics, university of science and technology of china, Hefei 2.002., china.

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关键词： Linear regression M-estimate strong consistency.

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,{2.chen xiru (graduate school,university of science and technology of china.beijing 1002.9,{2.

Consider the linear regression model Yi=xi′β+σiei,i=1,…,n,…,where E（ei）=0,E（eiej）=δij,012.?）σ2.（?）…and {xi} satisfies A1（?）sum from i=1 to n xixi′/n（?）A2.for n large,A1>0,A2.*** paper shows that ... 详细信息

Consider the linear regression model Yi=xi′β+σiei,i=1,…,n,…,where E（ei）=0,E（eiej）=δij,012./sup>（?）σ2./sub>2./sup>（?）…and {xi} satisfies A1（?）sum from i=1 to n xixi′/n（?）A2./sub>,for n large,A1>0,A2./sub>>*** paper shows that （i） ifσi2./sup>,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./sup>=∞;（ii）if{σi2./sup>}is only known to belong to the set {（h1,h2./sub>,…）∶01（?）h2./sub>（?）…,sum from i=1 to ∞ hi-1=∞},then no mean-square consistent linear estimate of β exists,and,if e1,e2./sub>,…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

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 {2. 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 2.002., china Department of Mathematics Graduate School Academia Sinica Beijing China Department of Mathematics York University Toronto Department of Mathematics University of Science and Technology of China Heifei 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.∞.

If in the linear model （1）the random errors e1, e2./sub>,...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./sup>=∞.

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 {2.s 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

Identification and removal of block ambiguities in sea surface wind field with scatterometers

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science china.Earth sciences 2009年第2期52卷 242-249页

作者： chen KeHai1,2. XIE XueTong3 & FANG Yu4 1 South china.Sea Institute of Oceanology, Chinese Academy of {2.s, Guangzhou 510301, china.2.graduate university of Chinese Academy of {2.s, beijing 100049, china.3 school of Electronic {2. and Engineering, National university of Defense {12., Changsha 410073, china.4 The Institute of Remote Sensing and GIS, Peking university, beijing 100871, china South china.Sea Institute of Oceanology Chinese Academy of Sciences Guangzhou China graduate university of Chinese Academy of {2.s Beijing China school of Electronic science and Engineering National University of Defense Technology Changsha China The Institute of Remote Sensing and GIS Peking University Beijing China

The solution of the current wind retrieval algorithm for scatterometers has several wind vector ambi-guities, due to the bi-harmonic relationship between normalized backscattering cross section and the relative wind direction and the existence of the measurement error. In order to remove the ambiguities for a unique wind field, a circular median filter approach (CMF) is usually adopted. But under the con-dition for clustering distribution of the false ambiguities in some local areas, the CMF fails and thus engenders block ambiguities, which degrade the precision of the retrieved wind field. For such a situation, a technique of identification and removal of the block ambiguities is presented to further optimize the retrieved wind field after CMF. It is demonstrated in experiment that this technique can identify and remove most of the block ambiguities.

关键词： scatterometer block ambiguity identification and removal