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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 finance, university of science and technology of china, hefei 230026, 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.

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.

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 department of statistics and finance, university of science and technology of china, hefei 230026, china department of Mathematics, Guangxi Teacher College, Manning 530001, china School of Mathematics and Information science Guangxi University Nanning China department of statistics and finance University of Science and Technology of China Hefei China department of Mathematics Guangxi Teacher College Nanning 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. departmentofstatisticsandfinance 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 finance, university of science & technology of china, hefei 230026, 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.

Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory

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science china Mathematics 2005年第10期48卷 1379-1394页

作者： WANG Dingcheng~1 SU Chun~2 & ZENG Yong~1 1. School of Management and School of Applied Mathematics,university of Electronic science and technology of china,Chengdu 610054,china 2. department of statistics and finance,university of science and technology of china,hefei 230026,china School of Management and School of Applied Mathematics University of Electronic Science and Technology of China Chengdu China department of statistics and finance University of Science and Technology of China Hefei China

This paper obtains the uniform estimate for maximum of sums of independent and heavy-tailed random variables with nonnegative random weights, which can be arbitrarily dependent of each other. Then the applications to ... 详细信息

关键词： dependent stochastic return, discount factor, heavy-tails, discrete time insurance risk model, maxima of randomly weighted sums, ruin probability, tail probabilities, uniformly asymptotic estimate.

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 statistics,university of science and technology of china,hefei 230026,china Cancer Research Institute Queen’s University Kingston Canada department of finance and statistics University of Science and Technology of China Hefei 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

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 finance 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

EMPIRICAL LIKELIHOOD RATIO CONFIDENCE INTERVALS FOR VARIOUS DIFFERENCES OF TWO POPULATIONS

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Systems science and Mathematical sciences 2000年第1期13卷 23-30页

作者： QIN Yong song ZHAO Lin cheng (department of statistics and finance, university of science and technology of china, hefei 230026, china) 中国科学技术大学统计与金融系安徽合肥 230026 中国科学技术大学统计与金融系安徽合肥

******etriccontexts.O...II--31hasintroducedempiricallikelihoodratiostatistics... 详细信息

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关键词： Empirical likelihood semi-empirical likelihood hypotheses tests Wilks’ theorem.