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Asymptotic properties for the semiparametric regression model with randomly censored data

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Science China Mathematics 1997年第9期40卷 945-957页

作者：王启华郑忠国 Institute of Applied Mathematics Chinese Academy of SciencesBeijing 100080China Department of Probability and Statistics Peking UniversityBeijing 100871China

Suppose that the patients’ survival times,Y,are random variables following the semiparametric regression model Y=Xβ+g(T)+ε,where (X,T) is a radom vector taking values in R×[0,1],β is an unknown parameter,g(·) is an unknown smooth regression function and εis the random error with zero mean and variance σ*** is assumed that (X,T) is independent of ε.The estimators βn and gm(·) ofβ and g(·) are defined,respectively,when the observations are randomly censored on the right and the censoring distribution is ***,it isshown that βm is asymptotically normal and gm(·) is weak consistence with rate Op(n-1/3).

关键词： random censorship semiparametric regression asymptotic normality.

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 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.

LAD estimation for nonlinear regression models with randomly censored data

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Science China Mathematics 2005年第7期48卷 880-897页

作者： ZHOU Xiuqing WANG Jinde School of Mathematics and Computer Science Nanjing Normal University Nanjing 210097 China Department of Mathematics Nanjing University Nanjing 210093 China Department of Mathematics Nanjing University Nanjing 210093 China

The least absolute deviations (LAD) estimation for nonlinear regression models with randomly censored data is studied and the asymptotic properties of LAD estimators such as consistency, boundedness in probability and asymptotic normality.are established. Simulation results show that for the problems with censored data, LAD estimation performs much more robustly than the least squares estimation.

关键词： randomly censored data, nonlinear regression model, LAD estimator, asymptotic normality.

On asymptotics of t-type regression estimation in multiple linear model

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Science China Mathematics 2004年第4期47卷 628-639页

作者： GUI HengjianDepartment of Mathematics, Beijing Normal University, Beijing 100875, China Department of Mathematics Beijing Normal University Beijing China

We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error *** marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.

关键词： t-type regression estimator, M-estimator, one-step estimate, consistency, asymptotic normality.

The arithmetic genus and extrinsic geometry of smooth projective variety

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Science China Mathematics 1998年第7期41卷 729-735页

作者：陈志华姚勤 Department of Applied Mathematics Tongji University Shanghai China

Some theorems concerning the projective normality.and extrinsic geometry on the smooth variety are proved under some supposed conditions related to the arithmetic genus of the smooth variety.

关键词： subvariety arithmetic genus projective normality.

Iterative weighted partial spline least squares estimation in semiparametric modeling of longitudinal data

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Science China Mathematics 2003年第5期46卷 724-735页

作者：孙孝前尤进红 Department of Mathematics Huaiyin Teachers College Huaian 223001 China Department of Statistics University of Missouri-Columbia Columbia MO 65211 USA Department of Mathematics and Statistics University of Regina Regina Saskatchewan Canada S4S 0A2

In this paper we consider the estimating problem of a semiparametric regression modelling whenthe data are longitudinal. An iterative weighted partial spline least squares estimator (IWPSLSE) for the para-metric component is proposed which is more efficient than the weighted partial spline least squares estimator(WPSLSE) with weights constructed by using the within-group partial spline least squares residuals in the senseof asymptotic variance. The asymptotic normality.of this IWPSLSE is established. An adaptive procedure ispresented which ensures that the iterative process stops after a finite number of iterations and produces anestimator asymptotically equivalent to the best estimator that can be obtained by using the iterative proce-dure. These results are generalizations of those in heteroscedastic linear model to the case of semiparametric regression.

关键词： semiparametric modelling, longitudinal data, iterative weighted partial spline leastsquares estimator (IWPSLSE), asymptotic normality.

Some large sample properties of an estimator of the hazard function from randomly censored data

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Chinese Science Bulletin 1995年第8期40卷 632-635页

作者：王启华 Department of Probability and Statistics Peking University Beijing 100871 China

In many lifetime studies, some of the subjects under study are censored on the righ bya prior censoring time. We observe only the censored data. It is important to estimatethe life characteristics of the subjects. Let T1, T2,…, Tn be independent and identically dis-tributed nonnegative random variables with common continuous distribution funtion F

关键词： weak convergence strong consistency asymptotic representation asymptotic normality.

Convergence on randomly trimmed sums with a ψ-mixing sample:

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Chinese Science Bulletin 1996年第18期41卷 1497-1500页

作者：林正炎 Department of Mathematics Hangzhou University Hangzhou 310028 China

where α_n and β_n are integers with 0≤α_n<β_n≤n. For an i.i.d, sequence {X_n}, many authors studied the asymptotic behavior of the trimmed sums T_n. In this note, we try extending the research extent in two directions. First, we assume that {X_n} is φ-***, α_n and β_n may be positive integer-valued random variables satisfying the convergence of the trimming fractions α_n/n and β_n/n to random variables α and β respectively with 0≤α<β≤1 in some sense. It seems to have not been studied for these two cases. A central limit theorem for this kind of randomly trimmed sum is established. Moreover we also show a strong law of large numbers.

关键词： randomly trimmed sums ψ-mixing a.s. convergence asymptotic normality.