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Empirical likelihood confidence regions of the parameters in a partially linear single-index model

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Science china Mathematics 2005年第10期48卷 1333-1348页

作者： XUE Liugen~1 & ZHU Lixing~2 1. college of applied sciences,beijing university of technology,beijing 100022,china 2. Department of Mathematics,Hong Kong Baptist university,Hong Kong,china 1. college of applied sciences Beijing University of Technology 100022 Beijing China 2. Department of Mathematics Hong Kong Baptist University Hong Kong China

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

关键词： partially linear single-index model, empirical likelihood, confidence region, chi-square distribution, coverage probability.

Empirical likelihood-based inference in a partially linear model for longitudinal data

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Science china Mathematics 2008年第1期51卷 115-130页

作者： XUE LiuGen~(1+) & ZHU LiXing~2 1 college of applied sciences, beijing university of technology, beijing 100022, china 2 Department of Mathematics, Hong Kong Baptist university, Hong Kong, china college of applied sciences Beijing University of Technology Beijing 100022 China Department of Mathematics Hong Kong Baptist University Hong Kong China

A partially linear model with longitudinal data is considered, empirical likelihood to infer- ence for the regression coefficients and the baseline function is investigated, the empirical log-likelihood ratios is proven to be asymptotically chi-squared, and the corresponding confidence regions for the pa- rameters of interest are then constructed. Also by the empirical likelihood ratio functions, we can obtain the maximum empirical likelihood estimates of the regression coefficients and the baseline function, and prove the asymptotic normality. The numerical results are conducted to compare the performance of the empirical likelihood and the normal approximation-based method, and a real example is analysed.

关键词： partially linear model empirical likelihood confidence region longitudinal data 62G05 62G15 62G20

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

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Acta Mathematica Scientia 2010年第3期30卷 677-687页

作者：田萍杨林薛留根 Department of Mathematics Xuchang University college of applied sciences Beijing University of Technology

In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.

关键词： Longitudinal data partially linear single-index model penalized spline strong consistency asymptotic normality

A new DNA algorithm to solve graph coloring problem

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Progress in Natural Science:Materials International 2007年第6期17卷 733-738页

作者： Jiang Xingpeng1, Li Yin2, Meng Ya3 and Meng Dazhi2(1. National Laboratory of Pattern Recognition,Institute of Automation, Chinese Academy of sciences, beijing 100080, china 2. college of applied sciences, beijing university of technology, beijing 100022, china 3. School of Science, beijing Institute of technology, beijing 100081, china) National Laboratory of Pattern Recognition Institute of Automation Chinese Academy of Sciences Beijing 100080 China college of applied sciences Beijing University of Technology Beijing 100022 China School of Science Beijing Institute of Technology Beijing 100081 China

Using a small quantity of DNA molecules and little experimental time to solve complex problems successfully is a goal of DNA computing. Some NP-hard problems have been solved by DNA computing with lower time complexity than conventional computing. However, this advantage often brings higher space complexity and needs a large number of DNA encoding molecules. One example is graph coloring problem. Current DNA algorithms need exponentially increasing DNA encoding strands with the growing of problem size. Here we propose a new DNA algorithm of graph coloring problem based on the proof of four-color theorem. This algorithm has good properties of needing a relatively small number of operations in polynomial time and needing a small number of DNA encoding molecules (we need only 6R DNA encoding molecules if the number of regions in a graph is R).

关键词： DNA computing NP-hard problem graph coloring problem.

Existence of solutions for the dynamic equation of ferrimagnets

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Progress in Natural Science:Materials International 2007年第11期17卷 1279-1283页

作者： Zeng Ming1, Guo Boling2 and Cheng Caozong1(1. college of applied sciences, beijing university of technology, beijing 100022, china 2. Center for Nonlinear Studies, Institute of applied Physics and Computational Mathematics, beijing 100088, china) college of applied sciences Beijing University of Technology Beijing 100022 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China

Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.

关键词： ferrimagnet weak solutions penalized method finite difference method

Approximation of dense-n/2-subgraph and table compression problems

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Science china Mathematics 2005年第9期48卷 1223-1233页

作者： XU Dachuan~1 HAN Jiye~2 & DU Dongle~3 1. college of applied sciences,beijing university of technology,beijing 100022,china 2. Institute of applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of sciences,beijing 100080,china 3. Faculty of Administration,university of New Brunswick,P.O.Box 4400,Fredericton,NB E3B 5A3,Canada college of applied sciences Beijing University of Technology Beijing 100022 China Institute of applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Faculty of Administration University of New Brunswick P.O. Box 4400 Fredericton NB E3B 5A3 Canada

We develop improved approximation algorithms for two NP-hard problems: the dense-n/2-subgraph and table *** on SDP relaxation and advanced rounding techniques,we first propose 0. 5982 and 0. 5970-approximation algorithms respec- tively for the dense-n/2-subgraph problem (DSP) and the table compression problem (TCP). Then we improve these bounds to 0. 6243 and 0. 6708 respectively for DSP and TCP by adding triangle inequalities to strengthen the SDP *** results for TCP beat the 0. 5 bound of a simple greedy algorithm on this problem,and hence answer an open question of Anderson in an affirmative way.

关键词： dense-n/2-subgraph problem(DSP) table compression problem(TCP) SDP approximation ratio

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

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Science china(Physics,Mechanics & Astronomy) 2007年第3期50卷 339-347页

作者： HUANG YongChang1,3,4, JIANG YunGuo1 & LI XinGuo2,3 1 Institute of Theoretical Physics, college of applied sciences, beijing university of technology, beijing 100022, china 2 Institute of Modern Physics, Chinese Academy of sciences, Lanzhou 730000, china 3 Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Collisions, Chinese Academy of sciences, Lanzhou 730000, china 4 china Center of Advanced Science and technology (World Laboratory), beijing 100080, china 1. Institute of Theoretical Physics College of Applied Sciences Beijing University of Technology Beijing 100022 China 3. Center of Theoretical Nuclear Physics National Laboratory of Heavy Ion Collisions Chinese Academy of Sciences Lanzhou 730000 China 4. china Center of Advanced Science and technology (World Laboratory) Beijing 100080 China 2. Institute of Modern Physics Chinese Academy of Sciences Lanzhou 730000 China

According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transforma- tions of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was ob- tained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propaga- tors were obtained.

关键词： supersymmetric electromagnetic interaction BRST quantization Ward identity

The influence of pump power on the spectral peak shift of whispering gallery modes

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The influence of pump power on the spectral peak shift of wh...

Approximation of dense-n/2-subgraph and table compression problems

2007亚洲光电子会议先进的传感系统与应用分会场

作者： Jiyou Wang*a , Fang Yuana, Lipu Wangb,Min Wanga (aThe college of applied sciences, beijing university of technology, beijing 100022, china bXingtai medical college, Xingtai, Hebei 054056,china)

In this paper, the glass microsphere co-doped Er3+/Yb3+ was fabricated. Many regularly spaced, sharp peaks appeared in the emission spectra of the glass microspere. We report the laser power induce the spectral shift of the whispering-gallery-modes [WGMs] of a glass sphere. The laser power dependence of the WGMs spectral position is about 0.0252nm/mW under 976nm excitation. Maybe, the glass microsphere can be used as a temperature sensor.

关键词： glass microsphere whispering gallery modes rare earth luminescence

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Approximation of dense-n/2-subgraph and table compression pr...