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Checking for normality in linear mixed models

Science china mathematics 2012年第4期55卷 787-804页

作者： WU Ping 1,,ZHU LiXing 2,3 & FANG Yun 4.1 school of finance and statistics,East china Normal {4.,Shanghai 20024.,china 2 school of statistics and mathematics,yunnan {4. of finance and Economics,yunnan 650221,china 3 The Department of mathematics,Hong Kong Baptist {4.,Hong Kong 999077,china 4.mathematics and Science College,Shanghai Normal {4.,Shanghai 200234.china 1. school of finance and statistics East China Normal University Shanghai 200241 China2. School of Statistics and Mathematics Yunnan University of Finance and Economics Yunnan 650221 China3. The Department of Mathematics Hong Kong Baptist University Hong Kong 999077 China4. Mathematics and Science College Shanghai Normal University Shanghai 200234 China

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

关键词： linear mixed models estimated best linear unbiased predictors BHEP tests conditional MonteCarlo test

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Asymmetric interaction will facilitate the evolution of cooperation

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Science china(Life Sciences) 2010年第8期53卷 1041-1046页

作者： WANG RuiWu1, HE JunZhou1,2, WANG YaQiang1,2, SHI Lei1,3 & LI YaoTang1,2 1 State Key Laboratory of Genetic Resources and Evolution, Kunming Institute of Zoology, Chinese Academy of Science, Kunming 650223, china 2 school of mathematics and statistics, {4. university, Kunming 650091, china 3 statistics and mathematics College, {4. university of finance and Economics, Kunming 650221, china 1. State Key Laboratory of Genetic Resources and Evolution Kunming Institute of Zoology Chinese Academy of Science Kunming 650223 China2. School of Mathematics and Statistics Yunnan University Kunming 650091 China3. Statistics and Mathematics College Yunnan University of Finance and Economics Kunming 650221 China

Explaining the evolution of cooperation remains one of the greatest problems for both biology and social science. The classical theories of cooperation suggest that cooperation equilibrium or evolutionary stable strategy between partners can be maintained through genetic similarity or reciprocity relatedness. These classical theories are based on an assumption that partners interact symmetrically with equal payoffs in a game of cooperation interaction. However, the payoff between partners is usually not equal and therefore they often interact asymmetrically in real cooperative systems. With the Hawk–Dove model, we find that the probability of cooperation between cooperative partners will depend closely on the payoff ratio. The higher the payoff ratio between recipients and cooperative actors, the greater will be the probability of cooperation interaction between involved partners. The greatest probability of conflict between cooperative partners will occur when the payoff between partners is equal. The results show that this asymmetric relationship is one of the key dynamics of the evolution of cooperation, and that pure cooperation strategy (i.e., Nash equilibrium) does not exist in asymmetrical cooperation systems, which well explains the direct conflict observed in almost all of the well documented cooperation systems. The model developed here shows that the cost-to-benefit ratio of cooperation is also negatively correlated with the probability of cooperation interaction. A smaller cost-to-benefit ratio of cooperation might be created by the limited dispersal ability or exit cost of the partners involved, and it will make the punishment of the non-cooperative individuals by the recipient more credible, and therefore make it more possible to maintain stable cooperation interaction.

关键词： Hawk–Dove game evolutionarily stable strategy asymmetric cooperation mixed strategy Nash equilibrium

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TESTING SPHERICITY IN A GMANOVA-MANOVA MODEL WITH NORMAL ERROR

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Acta Mathematica Scientia 2008年第3期28卷 639-650页

作者：白鹏石磊 statistics and mathematics College Yunnan University of Finance and Economics

This article presents a statistic for testing the sphericity in a GMANOVA- MANOVA model with normal error. It is shown that the null distribution of this statistic is beta and its nonnull distribution is given in seri... 详细信息

关键词： GMANOVA-MANOVA model sphericity test zonal polynomial

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The evolution of cooperation in asymmetric systems

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Science china(Life Sciences) 2010年第1期53卷 139-149页

作者： WANG RuiWu1 & SHI Lei2 1 State Key Laboratory of Genetic Resources and Evolution,Kunming Institute of Zoology,Chinese Academy of Science,Kunming 650223,china 2 statistics and mathematics College,yunnan {4. of finance and Economics,Kunming 650221,china 1. State Key Laboratory of Genetic Resources and Evolution Kunming Institute of Zoology Chinese Academy of Science Kunming 650223 China2. Statistics and Mathematics College Yunnan University of Finance and Economics Kunming 650221 China

Explaining the "Tragedy of the Commons" of the evolution of cooperation remains one of the greatest problems for both biology and social *** interaction,which is one of the most important characteristics of cooperative systems,has not been sufficiently considered in the existing models of the evolution of *** the inequality in the number and payoff between the cooperative actors and recipients in cooperation systems,discriminative density-dependent interference competition will occur in limited dispersal *** model and simulation show that the local but not the global stability of a cooperative interaction can be maintained if the utilization of common resource remains unsaturated,which can be achieved by density-dependent restraint or competition among the cooperative *** intense density dependent interference competition among the cooperative actors and the ready availability of the common resource,with a higher intrinsic contribution ratio of a cooperative actor to the recipient,will increase the probability of *** cooperation between the recipient and the cooperative actors can be transformed into conflict and,it oscillates chaotically with variations of the affecting factors under different environmental or ecological *** higher initial relatedness(*** to kin or reciprocity relatedness),which is equivalent to intrinsic contribution ratio of a cooperative actor to the recipient,can be selected for by penalizing less cooperative or cheating actors but rewarding cooperative individuals in asymmetric *** initial relatedness is a pivot but not the aim of evolution of *** explains well the direct conflict observed in almost all cooperative systems.

关键词： cooperation altruism density dependent tragedy of the commons oscillation chaos asymmetric interaction interference competition

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Almost sure central limit theorems for random functions

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Science china mathematics 2006年第12期49卷 1788-1799页

作者： LU Chuanrong, QIU Jin & XU Jianjun school of mathematics and statistics, Zhejiang university of {4. and Economics, Hangzhou 310018, china Department of mathematics, Zhejiang university, Hangzhou 310028, china 1. school of mathematics and statistics Zhejiang University of Finance and Economics Hangzhou 310018 China 2. Department of mathematics Zhejiang University Hangzhou 310028 China

Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|... 详细信息

Let {Xn,-∞2 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|Rn| 2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.

关键词： statistics,random function,almost sure central limit theorem,logarithm average.

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A Positive Analysis for BPR of the Third Party Logistics

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厦门大学学报（自然科学版） 2002年第S1期41卷 231-232页

作者： LI Yan-feng 1, WU Xiao-song 2 (1. Management school, Huazhong university of Science and Technology, Wuhan 4.0074. china 2. Information Management school, {4. university of finance and Trade, Kunming 650221, china)

Facing the opportunities and challenges of china’s en try into WTO, logistics enterprises take BPR as an important way to improve the core *** modern logistics is a systematic engineering and its require ments are the standardization and normalization for enhancing the Chinese enterp rises’ level of logistic *** paper reveal the importance of manageme nt technique,information technique and business model in enterprise’s BPR throug h the positive analysis for business process of the third party logistics as a new system after reengineering businees process. Reorganization of marketing target. The characters of business procedure after N ew Sunshine recomposed include: "the last mile " service systems of logistics; s etting up HUB to control many end-points in big and middle cities, setting up s ingle-points in small cities, the small parts acting delivering system which st yle of "assembly and allot" are made of in. Reorganization of business model. The New Sunshine reorganized has three aspects of business model which set up: HUB, end-point and single-point. Reorganization of business *** mainly business process of restructure Ne w Sunshine include : standard quote declaring prices to all attendants; on line, timely and exactly declaring prices; The net contract of B2C work on line; Tran smit to attendant; Logistice operating; feedback the working information; User t rack goods condition; Settling information; paying and so on, the different busi ness can separate into kinds of right corresponding to the business process, suc h as the picture of distributing parcel, ordering, moving, picking, transporting , delivering, information, inquiring and settling. Set up standard systems. Aims to execute standard management is to make distribu te and logistics for norm and standard, according to the resources share tog ether with the progresses especially and base on reducing the necessary expenses to reduce the living expenses, while low cost

关键词： third party logistics management technique info rmation technique business model

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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 {4.,Chengdu 610054.{4. 2. Department of statistics and finance,university of Science and Technology of {4.,Hefei 230026,{4. 1. school of Management and school of Applied mathematics University of Electronic Science and Technology of China 610054 Chengdu China 2. Department of statistics and finance University of Science and Technology of China 230026 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.

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Reengineering Model of Supply Chain of Tea Industry in yunnan

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厦门大学学报（自然科学版） 2002年第S1期41卷 230-231页

作者： LI Yan-feng 1, JIANG Fa-kui 2 (1. Management school, Huazhong university of Science and Technology, Wuhan 4.0074. china 2. Department of Business Administration, yunnan university of finance and Economics, Kunming 650221, china)

yunnan university of finance and Trade recording to t he statistics of chain’s output of tea, yunnan province has entered the ranks of the larger ones of the production in china. yunnan’s tea industry has the natur al resources and the economic effects envied, on the orther hand, yunnan’s tea m arket has gradually become less and the economic effects have been poor. Through our comprehensive investigation and study, we consider that because the supply chain has seriously been disjointed among production, supply and sale of tea ind ustry in yunnan, the supply chain of yunnan’s tea industry need to be reorganize d for the promoting the development of yunnan’s tea industry. The essence of reengineering of yunnan’s tea industrial supply chain is to set u p the model of the trailed operation,to strengthen the strategic partnership man agement between the supply chain, to optimize the design of the supply chain and build up and improve the working mechanism for management of the tea industrial supply chain. The structure of yunnan’s model of tea industrial supply chain: the model of com mercial flow; the model of logistics flow; the model of information flow and the model of cash flow. The solutions and policies for the reorganization of yunnan’s tea industrial sup ply chain: planning, logistics and distribution and sales. Set up the supporting system of information technology. Build up the control system of production and *** the working mechanism of yunnan’s tea industrial supply chain. Implement the engineering of exporting yunnan’s tea into the markets of other p rovinces and foreign markets. Have many the channels that raise the funds of dev elopment for yunnan’s tea industry.

关键词： yunnan tea industry reengineering supply chain building model

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Smooth solutions of non-linear stochastic partial differential equations driven by multiplicative noises

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Science china mathematics 2010年第11期53卷 2949-2972页

作者： ZHANG XiCheng school of mathematics and statistics, Wuhan university, Wuhan 4.0072, {4. 1. school of mathematics and statistics Wuhan University Wuhan 430072 China

In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2D Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.

关键词： smooth solutions stochastic partial differential equations stochastic Navier-Stokes equations

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Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails

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Science china mathematics 2010年第6期53卷 1421-1434页

作者： LIU Li school of mathematics and statistics,Wuhan university,Wuhan 4.0072,{4. 1. school of mathematics and statistics Wuhan University Wuhan 430072 China

This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying *** moderate deviations of partial sums are first *** results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.

关键词： moderate deviation extended negative dependence consistently varying tail random sum

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