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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 university,Shanghai 200241,china 2 school of statistics and mathematics,yunnan university of finance and economics,yunnan 650221,china 3 The Department of mathematics,Hong Kong Baptist university,Hong Kong 999077,china 4 mathematics and Science College,Shanghai Normal university,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, yunnan university, Kunming 650091, china 3 statistics and mathematics College, yunnan 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 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. 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 finance 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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Beurling's theorem and invariant subspaces for the shift on Hardy spaces

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Science china mathematics 2008年第1期51卷 131-142页

作者： QIU ZhiJian school of Economic mathematics, Southwestern university of finance and economics, Chengdu 610074, china 1. school of Economic mathematics Southwestern University of Finance and Economics Chengdu 610074 China

Let G be a bounded open subset in the complex plane and let H 2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1–1 with respect to the Lebesgue measure on ?D and if the Riemann map belongs to the weak-star closure of the polynomials in H ∞(W). Our main theorem states: in order that for each M ∈ Lat (M z ), there exist u ∈ H ∞(G) such that M = ∨{uνH 2(G)}, it is necessary and sufficient that the following hold:each component of G is a perfectly connected domainthe harmonic measures of the components of G are mutually singularthe set of polynomials is weak-star dense in H ∞(G).Moreover, if G satisfies these conditions, then every M ∈ Lat (M z ) is of the form uH 2(G), where u ∈ H ∞(G) and the restriction of u to each of the components of G is either an inner function or zero.

关键词： Hardy space invariant subspace shift operator 47B20 30H05 30E10 46E15

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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 430074, 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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Carleson Measures on Planar Sets

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Acta Mathematica Sinica,English Series 2009年第11期25卷 1881-1892页

作者： Zhijian QIU school of mathematics,Southwestern university of finance and economics,Chengdu 610074,P. R. china school of mathematics Southwestern University of Finance and Economics Chengdu 610074 P. R. China

In this paper, we investigate what are Carleson measures on open subsets in the complex plane. A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles. We call a domain G multi-nicely connected if there exists a circular domain W and a conformal map ψ from W onto G such that ψ is almost univalent with respect the arclength on δW. We characterize all Carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular. Our results suggest the extension of Carleson measures probably is up to this class of open subsets

关键词： Carleson measure circular domain harmonic measure multi-nicely connected domain

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Local asymptotic behavior of the survival probability of the equilibrium renewal model with heavy tails

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Science china mathematics 2005年第3期48卷 300-306页

作者： JIANG Tao & CHEN Yiqing school of finance. Nanjing university of finance and economics, Nanjing 210003, china school of economics and Management, Guangdong university of Technology, Guangzhou 510090, china 1. school of finance Nanjing University of Finance and Economics 210003 Nanjing China 2. school of economics and Management Guangdong University of Technology 510090 Guangzhou China

Recently, Tang established a local asymptotic relation for the ruin probability in the Cramer-Lundberg risk model. In this short note we extend the corresponding result to the equilibrium renewal risk model.

关键词： geometric sums, heavy-tailed distribution, ladder height, the equilibrium renewal model, the ruin probability.

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Approximate solutions to infinite dimensional LQ problems over infinite time horizon

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Science china mathematics 2006年第7期49卷 865-876页

作者： PAN Liping, ZHANG Xu & CHEN Qihong school of Mathematical Sciences, Fudan university, Shanghai 200433, china school of mathematics, Sichuan university, Chengdu 610064, china Department of Applied mathematics, Shanghai university of finance & economics, Shanghai 200433, china school of Mathematical Sciences Fudan University Shanghai 200433 China school of mathematics Sichuan University Chengdu 610064 China Department of Applied mathematics Shanghai University of Finance & Economics Shanghai 200433 China

This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense.

关键词： approximate solution LQ problem infinite dimensional infinite time hori-

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