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Jackknifed random weighting for Cox proportional hazards model

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science china Mathematics 2012年第4期55卷 775-786页

作者： LI Xiao 1 ,WU YaoHua 2.& TU DongSheng 1 1 Cancer Research Institute,Queen’s University,Kingston,Ontario K 7L 3N6,Canada 2.department of finance and {2.,University of science and technology of china,hefei 2.002.,china 1. Cancer Research Institute Queen’s University Kingston Ontario K7L 3N6 Canada2. Department of Finance and Statistics University of Science and Technology of China Hefei 230026 China

The Cox proportional hazards model is the most used statistical model in the analysis of survival time ***,a random weighting method was proposed to approximate the distribution of the maximum partial likelihood estimate for the regression coefficient in the Cox *** method was shown not as sensitive to heavy censoring as the bootstrap method in simulation studies but it may not be second-order accurate as was shown for the bootstrap *** this paper,we propose an alternative random weighting method based on one-step linear jackknife pseudo values and prove the second accuracy of the proposed *** Carlo simulations are also performed to evaluate the proposed method for fixed sample sizes.

关键词： Cox proportional hazards model jackknife random weighting second-order accuracy simulations survival data

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 {2., University of science and technology of china, hefei 2.002., china department of Mathematics, Graduate School of Chinese Academy of sciences, Beijing 100049, china department of statistics and {2. 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 {2., University of science and technology of china, hefei 2.002., china department of Mathematics, Graduate School of Chinese Academy of sciences, Beijing 100049, china 1. department of statistics and {2. 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.

THE ASYMPTOTICALLY OPTIMAL EMPIRICALBAYES ESTIMATION IN ONE WAY ANOVA MODEL

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Systems science and Mathematical sciences 1999年第1期12卷 13-22页

作者： WEI Laisheng (department of statistics and {2., University of science and technology of china, hefei 2.002., china) 中国科学技术大学统计系安徽合肥

Consider the one-way analysis of variance (ANOVA) model Yij=μ+αi+∈ij,i=1,…,a; j = 1,…,b, ∈ij～N(0, σ2.. By using the kernel estimation of multivariate density function and its partial derivatives and making use of the estimators of nuisance parameters μ and σ2. we construct the empirical Bayes (EB) estimators of parameter vector α = (α1,…，αa)T. Under the existence condition of the second order moment on prior distribution, we obtain their asymptotic optimality.

关键词： Asymptotic optimality empirical Bayes estimation one way ANOVA model.

Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

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science china Mathematics 2006年第2期49卷 145-157页

作者： YIN Changming, ZHAO Lincheng & WEI Chengdong School of Mathematics and Information science, Guangxi University, Manning 530004, china {2. of statistics and finance, University of science and technology of china, hefei 2.002., china {2. of Mathematics, Guangxi Teacher College, Manning 530001, china 1. School of Mathematics and Information science Guangxi University Nanning 530004 China 2. department of statistics and finance University of Science and Technology of China Hefei 230026 China 3. department of Mathematics Guangxi Teacher College Nanning 530001 China

In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.

关键词： generalized linear models quasi-likelihood estimates asymptotic normality strong consistency.

DISTRIBUTION FREE LAWS OF THEITERATED LOGARITHM FOR KERNELESTIMATOR OF REGRESSION FUNCTIONBASED ON DIRECTIONAL DATADISTRIBUTION FREE LAWS OF THEITERATED LOGARITHM FOR KERNELESTIMATOR OF REGRESSION FUNCTIONBASED ON DIRECTIONAL DATA

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Chinese Annals of Mathematics,Series B 2000年第4期21卷 489-498页

作者： WANGXIAOMING ZHAOLINCHENG WUYAOHUA departmentofstatistics ShanghaiUniversityofFinanceandEconomicsShanghai200433China. departmentofstatisticsand{2. UniversityofScienceandTechnologyofChinaHefei230026China.

The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of desig... 详细信息

关键词： Directional data Laws of the iterated logrithm Regression function kernel estimator Strong convergence rates

STATISTICAL INFERENCE FOR CONTAMINATION DISTRIBUTION

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Journal of Systems science & Complexity 2001年第3期14卷 311-321页

作者： WU Shanshan MIAO Baiqi (department of statistics and {2., University of science & technology of china, hefei 2.002., china) 中国科学技术大学安徽合肥 230026

For the contamination distribution model F (x) = (1 -α) F1 (x) +αF2.(x), the estimators of o and F1 (x) are studied when F2.(x) is known, and the strong consistency of the two estimators is proved. Then the rate of ... 详细信息

关键词： Contamination strong consistency.

Empirical likelihood confidence regions of the parameters in a partially linear single-index model

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science china Mathematics 2005年第10期48卷 1333-1348页

作者： XUE Liugen~1 & ZHU Lixing~2.1. College of Applied sciences,Beijing University of technology,Beijing 10002.,{2. 2. department of Mathematics,Hong Kong Baptist University,Hong Kong,{2. 1. College of Applied sciences Beijing University of Technology 100022 Beijing China 2. department of Mathematics Hong Kong Baptist University Hong Kong China

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

关键词： partially linear single-index model, empirical likelihood, confidence region, chi-square distribution, coverage probability.

LIMITING BEHAVIOR OF UNIFORM RECURSIVE TREES

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Acta Mathematica Scientia 2007年第3期27卷 515-521页

作者：苏淳冯群强刘杰 department of statistics and {2. University of Science and Technology of China

The authors consider the limiting behavior of various branches in a uniform recursive tree with size growing to infinity. The limiting distribution of ξn,m, the number of branches with size m in a uniform recursive tree of order n, converges weakly to a Poisson distribution with parameter 1/m with convergence of all moments. The size of any large branch tends to infinity almost surely.

关键词： Uniform recursive tree branch limiting behavior