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Hierarchical linear regression models for conditional quantiles

Science China mathematics 2006年第12期49卷 1800-1815页

作者： TIAN Maozai & CHEN Gemai School of statistics, Renmin university of China, Beijing 100872, China and Center for Applied statistics, Renmin university of China, Beijing 100872, China department of mathematics and statistics, university of calgary, canada School of statistics Renmin University of China Beijing China Center for Applied statistics Renmin University of China Beijing China department of mathematics and statistics University of Calgary Canada

The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models,but it cannot deal effectively with the data with a hierarchical *** practice,the existence of such data hierarchies is neither accidental nor ignorable,it is a common *** ignore this hierarchical data structure risks overlooking the importance of group effects,and may also render many of the traditional statistical analysis techniques used for studying data relationships *** the other hand,the hierarchical models take a hierarchical data structure into account and have also many applications in statistics,ranging from overdispersion to constructing min-max ***,the hierarchical models are virtually the mean regression,therefore,they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional ***,the estimated coefficient vector (marginal effects)is sensitive to an outlier observation on the dependent *** this article,a new approach,which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models,is *** the theoretical front,we also consider the asymptotic properties of the new method,obtaining the simple conditions for an n1/2-convergence and an asymptotic *** also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.

关键词： hierarchical quantile regression models,EQ algorithm,fixed effects,random effects,regression quantile.

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Normal Operators Similar to Irreducible Operators

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Acta Mathematica Sinica,English Series 1994年第2期10卷 132-135页

作者： Fong Chekao Jiang Chunlan department of mathematics and statistics Carleton university Ottawa, Ontario, canada department of mathematics Jilin university Jilin, 130023 China Carleton university Jilin university

A complete characterization of normal operators which are similar to irreducible operators and some related results are given.

关键词： Normal Operators Similar to Irreducible Operators Math

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NANOSTRUCTURES OF FUNCTIONAL BLOCK COPOLYMERS

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Chinese Journal of Polymer Science 2000年第3期18卷 255-262页

作者： Guojun Liu department of Chemistry, university of calgary, 2500 university Dr., NW, calgary, Alberta, canada T2N IN4 university of calgary 加拿大

Nanostructure fabrication from block copolymers in my group normally involves polymer design, synthesis, self-assembly, selective domain crosslinking, and sometimes selective domain removal. Preparation of thin films withnanochannels was used to illustrate the strategy we took. In this particular case, a linear triblock copolymer polyisoprenc-block-poly(2-cinnamoylethyl methacrylate)-block-poly(t-butyl acrylate), PI-b-PCEMA-b-PtBA, was used. Films, 25 to50 μm thick, were prepared from casting on glass slides a toluene solution of PI-b-PCEMA-b-PtBA and PtBA homopolymer,hPtBA, where hPtBA is shorter than the PtBA block. At the hPtBA mass faction of 20% relative to the triblock or the totalPtBA (hPtBA and PtBA block) volume fraction of 0.44, hPtBA and PtBA formed a seemingly continuous phase in the matrixof PCEMA and Pl. Such a block segregation pattern was locked in by photocrosslinking the PCEMA domain. Nanochannelswere formed by extracting out hPtBA with solvent. Alternatively. larger channels were obtained from extracting out hPtBAand hydrolyzing the t-butyl groups of the PtBA block. Such membranes were not liquid permeable but had gas permeabilityconstants ～6 orders of magnitude higher than that of low-density polyethylene films.

关键词： Nanostructures Block copolymers Nanochannel generation Self-Assembly Polyisoprene-b-poly(2-cinnanoylethyl methacrylate)-b-poly(t-butyl acrylate)

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Weighted Norm Inequalities for Some Singular Integral Operators

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Acta Mathematica Sinica,English Series 1994年第1期10卷 42-48页

作者： Dai Longxiang department of mathematics university of British Columbia canada department of mathematics University of British Columbia Canada

In this paper,we consider the related weighted boundedness of the operators which were studied by *** and *** de Francia.

关键词： In Math Weighted Norm Inequalities for Some Singular Integral Operators

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On hypothesis testing with a partitioned random alternative

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Science China mathematics 2010年第4期53卷 927-938页

作者： WANG WeiZhen department of mathematics and statistics,Wright State university,Dayton,OH 45435,USA department of mathematics and statistics Wright State University

It is common in statistical practice that one needs to make a choice among m + 1 mutually exclusive claims on *** m=1,it is done by the (traditional) hypothesis *** this paper,a generalization to the case m > 1 is *** fundamental difference with the case m=1 is that the new alternative hypothesis is a partition of m multiple claims and is *** is used to decide which claim in the partition is to be tested as the ***,a random alternative is *** conditional and overall type I errors of the proposed test are controlled at a given level,and this test can be used as a new solution for the general multiple test *** classical problems,including the one-sample problem,model selection in multiple linear regression,and multi-factor analysis,are revisited,and new tests are provided ***,the famous two-sided t-test should be replaced by the proposed.

关键词： analysis of variance conditional probability multiple linear regression one-sample problem

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Further Estimate of Complete Trigonometric Sums

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清华大学学报(自然科学版) 1989年第6NO.05NO.04NO.03NO.02NO.01期 74-85页

作者： Ding Ping (department of mathematics, Simon Fraser university, canada) Qi Minggao (department of Applied mathematics, Tsinghua university)

The following theorem is proved: Let f(x)=akxk+…a1x+a0 be a polynomial with integral coefficients such that(a1), …,ak, q)=1. where q is a positive integer. Then, for k≥3,

关键词： complete trigonometric sums polynominl with integral coefficients congruent equation

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Some results on resolvable incomplete block designs

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Science China mathematics 2005年第4期48卷 503-512页

作者： LIU Minqian & FANG Kaitai department of statistics, Nankai university, Tianjin 300071, China department of mathematics, Hong Kong Baptist university, Hong Kong, China department of statistics Nankai University Tianjin China department of mathematics Hong Kong Baptist University Hong Kong China

This paper is concerned with the uniformity of a certain kind of resolvable incomplete block (RIB for simplicity) design which is called the PRIB design here. A sufficient and necessary condition is obtained, under which a PRIB design is the most uniform in the sense of a discrete discrepancy measure, and the uniform PRIB design is shown to be connected. A construction method for such designs via a kind of U-type designs is proposed, and an existence result of these designs is given. This method sets up an important bridge between PRIB designs and U-type designs.

关键词： block design, discrepancy, orthogonal array, supersaturated design, U-type design.

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Weak martingale Hardy spaces and weak atomic decompositions

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Science China mathematics 2006年第7期49卷 912-921页

作者： HOU Youliang & REN Yanbo School of mathematics and statistics, Wuhan university, Wuhan 430072, China department of mathematics & Physics, Henan university of Science and Technology, Luoyang 471003, China School of mathematics and statistics Wuhan University Wuhan China department of mathematics & Physics Henan University of Science and Technology Luoyang China

In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms. They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory. And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved. With the help of the weak atomic decompositions of martingale, a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given. Using the sufficient condition, we obtain a series of martingale inequalities with respect to the weak Lp-norm, the inequalities of weak (p ,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces. These inequalities are the weak versions of the basic inequalities in the classical martingale Hp-theory.

关键词： martingale, weak Hardy space, weak atom, atomic decomposition.

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Weighted Profile Least Squares Estimation for a Panel Data Varying-Coefficient Partially Linear Model

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Chinese Annals of mathematics,Series B 2010年第2期31卷 247-272页

作者： Bin ZHOU Jinhong YOU Qinfeng XU Gemai CHEN School of Finance and statistics East China Normal University Shanghai 200241 China. department of statistics Shanghai University of Finance and Economics Shanghai 200433 China. Corresponding Author. School of Management Fudan University Shanghai 200433 China. department of mathematics and statistics University of Calgary Calgary Alberta T2N 1N4 Canada.

This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model （due to Baltagi 1995） to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator （WPLSE） and a weighted local polynomial estimator （WLPE） for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator （PLSE）, and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator （LPE）. The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll （2000） and Lin and Carroll （2000）, ignoring the correlation structure entirely and ＂pretending＂ that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups illustrate the finite sample performances of the Some simulation studies are conducted to proposed procedures.

关键词： Semiparametric Panel data Local polynomial Weighted estimation Block bootstrap

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The Willmore functional and the containment problem in R^4

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Science China mathematics 2007年第3期50卷 325-333页

作者： Jia-zu ZHOU School of mathematics and statistics, Southwest university, Chongqing 400715, China department of mathematics, Polytechnic university, Brooklyn, NY 11201, USA School of mathematics and statistics Southwest University Chongqing China department of mathematics Polytechnic University Brooklyn USA

Let∑be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional∫∑H2dσ. This bound is an invariant involving the area of∑, the volume and Minkowski quermassintegrals of the convex body that∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4.

关键词： mean curvature scalar curvature kinematic formula Minkowski quermassintegrals convex body convex hypersurface 52A22 53C65 51C16

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