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Efficient estimation for additive hazards regression with bivariate current status data

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Science china Mathematics 2012年第4期55卷 763-774页

作者： TONG XingWei 1,,HU Tao 2 & SUN JianGuo 3,4 1 school of mathematical sciences,beijing normal university,beijing 100875,china 2 school of mathematical sciences,Capital normal university,beijing 100048,china 3 school of Mathematics,Jilin university,Changchun 130012,china 4 Department of Statistics,university of Missouri,Columbia,MO 65211,USA school of mathematical sciences Beijing Normal University Beijing China school of mathematical sciences Capital Normal University Beijing China school of Mathematics Jilin University Changchun China Department of Statistics University of Missouri Columbia USA

This paper discusses efficient estimation for the additive hazards regression model when only bivariate current status data are available. Current status data occur in many fields including demographical studies and tumorigenicity experiments （Keiding, 1991; Sun, 2006） and several approaches have been proposed for the additive hazards model with univariate current status data （Linet M., 1998; Martinussen and Scheike, 2002）. For bivariate data, in addition to facing the same problems as those with univariate data, one needs to deal with the association or correlation between two related failure time variables of interest. For this, we employ the copula model and an efficient estimation procedure is developed for inference. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. An illustrative example is provided.

关键词： bivariate current status data copula model counting processes efficient estimation joint survivalfunction

Characterization for commutators of n-dimensional fractional Hardy operators

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Science china Mathematics 2007年第10期50卷 1418-1426页

作者： Zun-wei FU~(1,2) Zong-guang LIU~3 Shan-zhen LU~(1+) Hong-bin WANG~3 ~1 school of mathematical sciences,beijing normal university,beijing 100875,china ~2 Department of Mathematics,Linyi normal university,Linyi 276005,china ~3 Department of Mathematics,china university of Mining and Technology (beijing),beijing 100083,china school of mathematical sciences Beijing Normal University Beijing China Department of Mathematics Linyi Normal University Linyi China Department of Mathematics China University of Mining and Technology (Beijing) Beijing China

In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^... 详细信息

关键词： n-dimensional fractional Hardy operator, commutator, C(M)O function, homogeneous Herz space

Twisted exponential sums of polynomials in one variable

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Science china Mathematics 2010年第9期53卷 2395-2404页

作者： LIU ChunLei1,& LIU WenXin2,3 1Department of Mathematics,Shanghai Jiao Tong university,Shanghai 200240,china 2Department of Fundamental Subject,Tianjin Institute of Urban Construction,Tianjin 300384,china 3school of mathematical sciences,beijing normal university,beijing 100875,china Department of Mathematics Shanghai Jiao Tong University Shanghai China Department of Fundamental Subject Tianjin Institute of Urban Construction Tianjin China school of mathematical sciences Beijing Normal University Beijing China

The twisted T-adic exponential sums associated to a polynomial in one variable are *** explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the C-function of the twisted T-adic exponential *** bound gives lower bounds for the Newton polygon of the L-function of twisted p-power order exponential sums.

关键词： exponential sum L-function Newton polygon

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 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

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 school of mathematical sciences Beijing Normal University Beijing 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

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 school of mathematical sciences Beijing Normal University Beijing 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

Commutators of pseudo-differential operators

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Science china Mathematics 2008年第3期51卷 453-460页

作者： LIN Yan school of mathematical sciences, beijing normal university, beijing 100875, china school of mathematical sciences Beijing Normal University Beijing China

In this paper, the boundedness of commutators generated by pseudo-differential operators and BMO functions is discussed on Lebesgue spaces.

关键词： pseudo-differential operator BMO function commutator Lebesgue space 42B20 35S05 47G30

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 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

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 school of mathematical sciences Beijing Normal University Beijing 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