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The restricted EM algorithm under linear inequalities in a linear model with missing data

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Science china mathematics 2005年第6期48卷 819-828页

作者： ZHENG Shurong, SHI Ningzhong & GUO Jianhua school of mathematics and statistics, northeast normal university, changchun 130024, china Institute of mathematics, Jilin university, changchun 130012, china 1. school of mathematics and statistics Northeast Normal University 130024 Changchun China 2. Institute of mathematics Jilin University 130012 Changchun China

This paper discusses the maximum likelihood estimate of β under linear inequalities A0β≥ a in a linear model with missing data, proposes the restricted EM algo rithm and proves the convergence.

关键词： EM algorithm, linear model, maximum likelihood estimate, missing data.

Global Existence of Classical Solutions for Some Oldroyd-B Model via the Incompressible Limit

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Chinese Annals of mathematics,Series B 2006年第5期27卷 565-580页

作者： Zhen LEI school of Mathematical Sciences, Fudan university, Shanghai 200433, china school of mathematics and statistics, northeast normal university, changchun 130024, china. school of Mathematical Sciences Fudan University Shanghai 200433 China school of mathematics statistics Northeast Normal University Changchun 130024 China

In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data ... 详细信息

关键词： Incompressible limit Global existence Oldroyd model

Infinite-dimensional Hamiltonian Lie superalgebras

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Science china mathematics 2010年第6期53卷 1625-1634页

作者： MU Qiang1,2 & ZHANG YongZheng1,1school of mathematics and statistics,northeast normal university,changchun 130024.china 2school of mathematics,Harbin normal university,Harbin 150025,china 1. school of mathematics and statistics Northeast Normal University Changchun 130024 China2. School of Mathematics Harbin Normal University Harbin 150025 China

The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent *** are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.

关键词： Hamiltonian superalgebra filtration automorphism

OPTIMAL CONTROL OF MULTISOLUTION ORDINARY DIFFERENTIAL EQUATIONS IN THE ABSENCE OF CONVEXITY

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Journal of Systems Science & Complexity 2010年第2期23卷 321-333页

作者： Shu LUAN Hang GAO school of mathematics and Computation Science Zhanjiang Normal College Zhanjiang 524048 China. school of mathematics and statistics Northeast Normal University Changchun 130024 China.

In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of *** overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are *** the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is *** the end of this paper,the authors discuss the applicationof the maximum principle by an example.

关键词： Multisolution ODEs optimal control Pontryagin's maximum principle relaxed controls.

Split-plot designs with general minimum lower-order confounding

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Science china mathematics 2010年第4期53卷 939-952页

作者： WEI JiaLin 1,4,YANG JianFeng 1,LI Peng 3 & ZHANG RunChu 1,2,1 school of Mathematical Sciences and LPMC,Nankai university,Tianjin 300071,china 2 klas and school of mathematics and statistics,northeast normal university,changchun 130024.china 3 school of Mathematical Sciences,Capital normal university,Beijing 100037,china 4 school of Sciences,Tianjin university of Commerce,Tianjin 300134,china 1. school of Mathematical Sciences and LPMC Nankai University Tianjin 300071 China4. School of Sciences Tianjin University of Commerce Tianjin 300134 China3. School of Mathematical Sciences Capital Normal University Beijing 100037 China2. KLAS and School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

Split-plot designs have been widely used in industrial *** to now,most methods for choosing this kind of designs are based on the minimum aberration (MA) ***,by introducing a new pattern,called aliased effect-number pattern (AENP),Zhang et *** a general minimum lowerorder confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) *** is proved that,the GMC criterion selects optimal designs in a more elaborate manner than the existing ones,and when an experimenter has a prior about the importance ordering of factors in experiments the GMC designs are better than other optimal *** this paper we extend the GMC criterion to the split-plot design case and give a GMC-FFSP criterion for ranking split-plot *** comparisons of the new criterion with the MA-MSA-FFSP criterion are given,and the optimal 32-run split-plot designs up to 14 factors under the two criteria are tabulated for comparison and application.

关键词： fractional factorial design GMC criterion minimum aberration split-plot

Revisit of Sheppard corrections in linear regression

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Science china mathematics 2010年第6期53卷 1435-1451页

作者： LIU TianQing1,ZHANG BaoXue1,HU GuoRong1 & BAI ZhiDong1,2,1Key Laboratory for Applied statistics of MOE and school of mathematics and statistics,northeast normal university,changchun 130024.china 2Department of statistics and Applied Probability,National university of Singapore,Singapore 117543,Singapore 1. Key Laboratory for Applied statistics of MOE and school of mathematics and statistics Northeast Normal University Changchun 130024 China2. Department of Statistics and Applied Probability National University of Singapore Singapore 117543 Singapore

Dempster and Rubin(D&R) in their JRSSB paper considered the statistical error caused by data rounding in a linear regression model and compared the Sheppard correction,BRB correction and the ordinary LSE by *** asymptotic results when the rounding scale tends to 0 were also *** a previous research,we found that the ordinary sample variance of rounded data from normal populations is always inconsistent while the sample mean of rounded data is consistent if and only if the true mean is a multiple of the half rounding *** the light of these results,in this paper we further investigate the rounding errors in linear *** notice that these results form the basic reasons that the Sheppard corrections perform better than other methods in D&R examples and their conclusion in general cases is *** in which the Sheppard correction works worse than the BRB correction are also ***,we propose a new approach to estimate the parameters,called "two-stage estimator",and establish the consistency and asymptotic normality of the new estimators.

关键词： asymptotic normality consistency linear regression model rounded data two-stage estimates

Efficient estimation for additive hazards regression with bivariate current status data

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Science china mathematics 2012年第4期55卷 763-774页

作者： TONG XingWei 1,,HU Tao 2 & SUN JianGuo 3,4 1 school of Mathematical Sciences,Beijing normal university,Beijing 100875,china 2 school of Mathematical Sciences,Capital normal university,Beijing 100048,china 3 school of mathematics,Jilin university,changchun 130012,china 4 Department of statistics,university of Missouri,Columbia,MO 65211,USA 1. school of Mathematical Sciences Beijing Normal University Beijing 100875 China2. School of Mathematical Sciences Capital Normal University Beijing 100048 China3. School of Mathematics Jilin University Changchun 130012 China4. Department of Statistics University of Missouri Columbia MO 65211 USA

This paper discusses efficient estimation for the additive hazards regression model when only bivariate current status data are available. Current status data occur in many fields including demographical studies and tumorigenicity experiments （Keiding, 1991; Sun, 2006） and several approaches have been proposed for the additive hazards model with univariate current status data （Linet M., 1998; Martinussen and Scheike, 2002）. For bivariate data, in addition to facing the same problems as those with univariate data, one needs to deal with the association or correlation between two related failure time variables of interest. For this, we employ the copula model and an efficient estimation procedure is developed for inference. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. An illustrative example is provided.

关键词： bivariate current status data copula model counting processes efficient estimation joint survivalfunction

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中美高师中学数学教学论教材比较及启示

外国教育研究 2006年第2期33卷 61-64页

作者：李清东北师范大学数学与统计学院吉林长春130024

中学数学教学论是我国高师数学教育类课程的一门主要课程,对这门课程的中美教材进行比较分析,对中学数学教师的职前专业发展具有重要意义。文章通过比较分析发现,中美高师中学数学教学论教材在知识内容、体系结构、能力培养、非智力因... 详细信息

中学数学教学论是我国高师数学教育类课程的一门主要课程,对这门课程的中美教材进行比较分析,对中学数学教师的职前专业发展具有重要意义。文章通过比较分析发现,中美高师中学数学教学论教材在知识内容、体系结构、能力培养、非智力因素培养、适应水平等方面都存在着较大的差异,对这些差异的对比研究可以为解决我国当前中学数学教学论课程的教材中存在的问题提供有益的启示。

关键词：中国美国中学数学教学论教材

Controllability of Quasilinear Parabolic Equations and Application

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Controllability of Quasilinear Parabolic Equations and Appli...