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Hierarchical linear regression models for conditional quantiles

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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 100872 China Department of Mathematics statistics University of Calgary Canada Center for Applied statistics Renmin University of China Beijing 100872 China

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.

Nonlinear autoregressive models with heavy-tailed innovation

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Science china Mathematics 2005年第3期48卷 333-340页

作者： JIN Yang & AN Hongzhi school of statistics, renmin university of china, beijing 100872, china Academy of Mathematics and Systems Science, Chinese Academy of Sciences, beijing 100080, china Sch. of statistics Renmin Univ. of China Beijing 100872 China Acad. of Mathematics and Syst. Sci. Chinese Acad. of Sci. Beijing 100080 China

In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlinear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.

关键词： nonlinear autoregressive model, innovation, tail probability.

Ruin probability of the renewal model with risky investment and large claims

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Science china Mathematics 2009年第7期52卷 1539-1545页

作者： WEI Li school of Finance,renmin university of china,beijing 100872,china 1. school of Finance Renmin University of China Beijing 100872 China

The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this *** claim sizes with common distribution of extended regular variation,we study the asymptotic behaviour of the ruin *** a corollary,we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims.

关键词： asymptotics extended regular variation renewal risk model risky investment strategy ruin probability 60G70 60K30 60K37

ENERGY FLOWS IN COMPLEX ECOLOGICAL SYSTEMS:A REVIEW

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Journal of Systems Science & Complexity 2009年第3期22卷 345-359页

作者： Jiang ZHANG Department of Systems Science,school of Management,beijing Normal university,beijing 100875,china. Department of Systems Science School of Management Beijing Normal University Beijing 100875 China

Energy flow drives the complex systems to *** allometric scaling as the universalenergy flow pattern has been found in different scales of ecological *** reflects the generalpower law relationship between flow and *** underlying mechanisms of energy flow patterns areexplained as the branching transportation networks which can be regarded as the result of systematicoptimization of a biological target under *** flows in the ecological system may bemodelled by the food web model and population dynamics on the *** paper reviews thelatest progress on the energy flow patterns,explanatory models for the allometric scaling and modellingapproach of flow and network evolution dynamics in ***,the possibility of generalizingthese flow patterns,modelling approaches to other complex systems is discussed.

关键词： Allometric scaling energy flow flows in complex systems food web.

On the weak convergence of super-Brownian motion with immigration

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Science china Mathematics 2009年第9期52卷 1875-1886页

作者： ZHANG Mei school of Mathematical Sciences, beijing Normal university, beijing 100875, china school of Mathematical Sciences Beijing Normal University Beijing 100875 China

We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting proc... 详细信息

关键词： super-Brownian motion with immigration occupation time process central limit theorem tightness 60J80 60F05

Multipliers and Herz type spaces

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Science china Mathematics 2008年第10期51卷 1919-1936页

作者： LU ShanZhen school of Mathematical Sciences, beijing Normal university, beijing 100875, china school of Mathematical Sciences Beijing Normal University Beijing 100875 China

Hrmander condition for boundedness of multiplier operators will be replaced by a weaker condition described by certain weighted or non-weighted Herz spaces. Some results on boundedness of multiplier operators are then established. As direct corollaries of main theorems in this paper, several celebrated results on boundedness of multiplier operators will be improved or deduced.

关键词： multiplier Herz space Herz type Hardy space 42B15 42B30 42B35

Infinitely many radial solutions to elliptic prob-lems with critical Sobolev and Hardy terms

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Science china Mathematics 2008年第9期51卷 1609-1618页

作者： TANG ZhongWei school of Mathematical Sciences, beijing Normal university, beijing 100875, china 1. school of Mathematical Sciences Beijing Normal University Beijing 100875 China

Let Ω ? ? N be a ball centered at the origin with radius R > 0 and N ? 7, 2* = $ \frac{{2N}} {{N - 2}} $ . We obtain the existence of infinitely many radial solutions for the Dirichlet problem ?Δu = $ \frac{\mu } {{|x|^2 }}u + |u|^{2^* - 2} u + \lambda u $ in Ω, u = 0 on ?Ω for suitable positive numbers μ and λ. Such solutions are characterized by the number of their nodes.

关键词： nodal solutions compactness critical Sobolev and Hardy terms 35J60 35B33

Hausdorff measures of the image, graph and level set of bifractional Brownian motion

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Science china Mathematics 2010年第11期53卷 2973-2992页

作者： LUAN NaNa school of Mathematical Sciences, beijing Normal university, beijing 100875, china 1. school of Mathematical Sciences Beijing Normal University Beijing 100875 China

Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of BH,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.

关键词： bifractional Brownian motion self-similar Gaussian processes image graph level set local time Hausdorff dimension Hausdorff measure

Some scaled limit theorems for an immigration super-Brownian motion

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Science china Mathematics 2008年第2期51卷 203-214页

作者： ZHANG Mei school of Mathematical Sciences,beijing Normal university,beijing 100875,china 1. school of Mathematical Sciences Beijing Normal University Beijing 100875 China

In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue *** first prove a functional central limit theorem,and then study the l... 详细信息

关键词： super-Brownian motion with immigration functional central limit theorem large deviation moderate deviation 60J80 60F05