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Unbiased Quasi-regression

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Chinese Annals of Mathematics,Series B 2007年第2期28卷 177-186页

作者： Guijun YANG Lu LIN runchu zhang Department of Statistics Tianjin University of Finance and Economics Tianjin 300222 China School of Mathematics and System Sciences Shandong University Jinan 250100 China. LPMC and School of Mathematical Sciences Nankai University Tianjin 300071 China.

Quasi-regression, motivated by the problems arising in the computer experiments, focuses mainly on speeding up evaluation. However, its theoretical properties are unexplored systemically. This paper shows that quasi-regression is unbiased, strong convergent and asymptotic normal for parameter estimations but it is biased for the fitting of curve. Furthermore, a new method called unbiased quasi-regression is proposed. In addition to retaining the above asymptotic behaviors of parameter estimations, unbiased quasi-regression is unbiased for the fitting of curve.

关键词： Computer experiment Quasi-regression Unbiasedness Fitting of curve Asymptotic normality

Bounds on the maximum numbers of clear two-factor interactions for 2^((n1+n2)-(k1+k2)) fractional factorial split-plot designs

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Science China Mathematics 2006年第12期49卷 1816-1829页

作者： ZI Xuemin zhang runchu LIU Minqian Department of Statistics School of Mathematical Sciences and LPMCNankai UniversityTianjin 300071China Department of StatisticsSchool of Mathematical Sciences and LPMCNankai UniversityTianjin 300071China Department of StatisticsSchool of Mathematical Sciences and LPMCNankai UniversityTianjin 300071China

Fractional factorial split-plot (FFSP) designs have an important value of investigation for their special *** are two types of factors in an FFSP design: the whole-plot (WP) factors and sub-plot (SP) factors,which can form three types of two-factor interactions:WP2fi,WS2fi and *** paper considers FFSP designs with resolution Ⅲ or Ⅳ under the clear effects *** derives the upper and lower bounds on the maximum numbers of clear WP2fis and WS2fis for FFSP designs,and gives some methods for constructing the desired FFSP *** further examines the performance of the construction methods.

关键词： fractional factorial design,split-plot,clear effects criterion,resolution.

Some results on 4~m2~n designs with clear two-factor interaction components

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Science China Mathematics 2008年第7期51卷 1297-1314页

作者： ZHAO ShengLi zhang runchu LIU MinQian School of Mathematical Sciences Qufu Normal UniversityQufu 273165China Department of Statistics School of Mathematical Sciences and Key Laboratory of Pure Mathematics and CombinatoricsNankai UniversityTianjin 300071China

Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs,and it has become an active research issue in recent *** et *** upper and lower bounds on the maximum number of clear two-factor interactions(2fi's) in 2n-(n-k) fractional factorial designs of resolutions III and IV by constructing a 2n-(n-k) design for given k,which are only restricted for the symmetrical *** paper proposes and studies the clear effects problem for the asymmetrical *** improves the construction method of Tang et *** 2n-(n-k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction components(2fic's) in 4m2n designs with resolutions III and *** lower bounds are achieved by constructing specific *** show that the number of clear 2fic's in the resulting design attains its maximum number in many cases,which reveals that the construction methods are satisfactory when they are used to construct 4m2n designs under the clear effects criterion.

关键词： clear mixed levels resolution two-factor interaction component 62K15

Weak minimum aberration and maximum number of clear two-factor interactions in 2_(IV)^(m-p)designs

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Science China Mathematics 2005年第11期48卷 1479-1487页

作者： YANG Guijun,LIU Minqian & zhang runchu Department of Statistics, Tianjin University of Finance and Economics, Tianjin 300222, China Department of Statistics, School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China 1. Department of Statistics Tianjin University of Finance and Economics 300222 Tianjin China 2. Department of Statistics School of Mathematical Sciences and LPMC Nankai University 300071 Tianjin China

Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it is proved that some 2IVm-p designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs. And some conditions are provided, under which a 2IVm-p design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time. Some weak minimum aberration 2IVm-p designs are provided for illustrations and two non-isomorphic weak minimum aberration 2IV13-6 designs are constructed at the end of this paper.

关键词： clear weak minimum aberration resolution wordlength pattern.

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具有特定纯净效应折中设计的若干理论及构造

中国科学：数学 2021年第5期51卷 763-772页

作者：王东莹张润楚吉林财经大学统计学院长春130117 南开大学数学科学学院天津100002 东北师范大学数学与统计学院长春130024

许多因析试验中,试验者只关心指定的一部分因子效应的估计效果.针对此类问题,Addelman(1962)首次提出了折中设计的方法,并定义纯净折中设计以保证指定的因子效应被有效地估计出来,但此类纯净折中设计的分辨度限定Ⅲ为Ⅳ.本文研究了四类... 详细信息

许多因析试验中,试验者只关心指定的一部分因子效应的估计效果.针对此类问题,Addelman(1962)首次提出了折中设计的方法,并定义纯净折中设计以保证指定的因子效应被有效地估计出来,但此类纯净折中设计的分辨度限定Ⅲ为Ⅳ.本文研究了四类全新的折中设计,指定因子效应的集合分别记为{G_(1);G_(1)×G_(1)}、{G_(1);G_(1)×G_(1);G_(2)×G_(2)}、{G_(1);G_(1)×G_(1);G_(1)×G_(2)}和{G_(1);G_(1)×G_(2)}.相应地,可以定义四种类型的纯净折中设计,即指定因子效应全部纯净的设计.本文研究四类纯净折中设计的存在性和结构特性,给出一些理论结果和具体的构造方法.构造结果表明新型的纯净折中设计的分辨度为Ⅲ或Ⅳ,并且与Addelman(1962)提出的纯净折中设计相比具有更多的纯净两阶交互效应.

关键词：折中设计纯净效应部分因析设计

MARKOV PROPERTIES OF THE GENERALIZED BROWNIAN SHEET AND EXTENDED OUP2

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Science in China,Ser.A 1985年第8期 814-825页

作者：张润楚 Department of Mathematics Nankai University Tianjin

In this paper, we introduce a class of generalized Brownian sheets and extend the OUP2 in [1]. By studying some fundamental properties of the former process, we first derive some of simple relaxed past Markov properties of the two processes, Next, utilizing the xelation between the two processes, we successively prove that, for two kinds of general sets, they possess the general relaxed past Markov properties and the Lévy Markov properties respectively. As a result, we conclude that the OUP2 in [1] also has the general Markov properties for the corresponding sets.

关键词：吉门 MARKOV PROPERTIES OF THE GENERALIZED BROWNIAN SHEET AND EXTENDED OUP2

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类保持投影(英文)

南开大学学报（自然科学版） 2005年第4期38卷 73-77,89页

作者：李长国张润楚南开大学数学科学学院

给出了一种高维数据可视化方法——类保持映射.即在对高维数据投影过程中,强调类的数目尽量保持.在对原数据点间距离加以适当权重后,这种投影方向给出了距离损失最小的二维构图.模拟表明此程序是主分量分析的扩展,且优于塞曼算法.

关键词：多维标度分析塞曼映射主分量分析聚类分析

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低偏差OALHD的构造

应用概率统计 2001年第2期17卷 149-155页

作者：马长兴张润楚南开大学数学科学学院统计学系天津300071

本文给出了利用均匀设计和正交表构造低偏差ＯＡＬＨ设计的方法，该方法构造的设计既有优良的均匀性又具有正交设计的均衡性，一个更重要的优点是可以构造较大样本容量的设计点集。本文同时给出了某些参数的均匀设计表，这些设计优于... 详细信息

本文给出了利用均匀设计和正交表构造低偏差ＯＡＬＨ设计的方法，该方法构造的设计既有优良的均匀性又具有正交设计的均衡性，一个更重要的优点是可以构造较大样本容量的设计点集。本文同时给出了某些参数的均匀设计表，这些设计优于现有的均匀设计，具有实用价值．

关键词：布点偏差均匀设计 OA-Based Latin Hypercube设计低偏差均匀LH设计均匀LH抽样 OALHD设计

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高维数据判别分析中的特征选择

数学物理学报（A辑） 2006年第5期26卷 647-652页

作者：谭鲜明张润楚南开大学数学学院天津300071

对高维数据进行判别分析,典型的策略包含数据压缩、特征提取与特征选择三步．该文对于选择合适的特征进行判别分析提出了一个定理,并应用这个定理对常用的主成分判别方法作了改进．最后,作者把改进的方法与两种常用的方法应用于一个神... 详细信息

对高维数据进行判别分析,典型的策略包含数据压缩、特征提取与特征选择三步．该文对于选择合适的特征进行判别分析提出了一个定理,并应用这个定理对常用的主成分判别方法作了改进．最后,作者把改进的方法与两种常用的方法应用于一个神经生理试验数据的判别分析．结果表明,在保证判别能力的同时,改进后的方法下用于判别的特征减少了．

关键词：判别分析高维数据主成分分析离散小波变换最优特征子集