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DISCRIMINANT ANALYSIS BASED ON STATISTICAL DEPTH

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Journal of systems Science & complexity 2010年第2期23卷 362-371页

作者： Jiao JIN·Hengjian CUI school of mathematical sciences,Key laboratory of mathematics and complex systems,ministry of education, beijing normal university,beijing 100875,china. school of mathematical sciences Key Laboratory of Mathematics and Complex Systems Ministry of Education

In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been *** this paper,a new depthfunction family that meets four properties mentioned in Zuo and Serfling(2000)is *** aclassification rule based on the depth function family is *** classification parameter b couldbe modified according to the type-Ⅰ error α,and the estimator of b has the consistency and achievesthe convergence rate n^(-1/2).With the help of the proper selection for depth family parameter c,theapproach for discriminant analysis could minimize the type-Ⅱ error β.A simulation study and a realdata example compare the performance of the different discriminant methods.

关键词： Depth discriminant analysis location parameter MVE scatter matrix.

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration

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Science china.mathematics 2008年第3期51卷 343-350页

作者： HONG WenMing school of mathematical sciences, laboratory of mathematics and complex systems, ministry of education,beijing normal university, beijing 100875, china school of mathematical sciences Laboratory of Mathematics complex systems Ministry of Education Beijing Normal University Beijing 100875 China

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).

关键词： super-Brownian motion large deviation moderate deviation random immigration Primary 60J80 Secondary 60F05

Convergence rates for reversible Markov chains without the assumption of nonnegative definite matrices

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Science china.mathematics 2010年第8期53卷 1979-1988页

作者： MAO Yong-Hua school of mathematical sciences,beijing normal university,laboratory of mathematics and complex systems,ministry of education,beijing 100875,china 1. school of mathematical sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China

Explicit convergence rates in geometric and strong ergodicity for denumerable discrete time Markov chains with general reversible transition matrices are obtained in terms of the geometric moments or uniform moments of the hitting times to a fixed *** way by Lyapunov's drift conditions is also used to derive these convergence *** a typical example,the discrete time birth-death process(random walk) is studied and the explicit criteria for geometric ergodicity are presented.

关键词： Markov chain spectral theory convergence rate geometric ergodicity strong ergodicity Lyapunov’s condition

Relative n-widths of periodic convolution classes with NCVD-kernel and B-kernel

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Science china.mathematics 2010年第1期53卷 165-172页

作者： YANG Wei & LIU YongPing school of mathematical sciences,beijing normal university laboratory of mathematics and complex systems,ministry of education,beijing 100875,china 1. school of mathematical sciences Beijing Normal University laboratory of mathematics and complex systems Ministry of Education Beijing 100875 China

In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q a... 详细信息

关键词： relative n-width periodic convolution class NCVD-kernel B-kernel

Sieve M-estimation for semiparametric varying-coefficient partially linear regression model

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Science china.mathematics 2010年第8期53卷 1995-2010页

作者： HU Tao 1,2 & CUI HengJian 1,2 1 school of mathematical sciences,beijing normal university,laboratory of mathematics and complex systems,ministry of education,beijing 100875,china.2 school of mathematical sciences,Capital normal university,beijing 100048,china 1. school of mathematical sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China2. School of Mathematical Sciences Capital Normal University Beijing 100048 China

This article considers a semiparametric varying-coefficient partially linear regression *** semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are *** main object is to estimate the nonparametric component and the unknown parameters *** is easier to compute and the required computation burden is much less than the existing two-stage estimation ***,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally *** experiments are carried out to investigate the performance of the proposed method.

关键词： partly linear model varying-coefficient robustness optimal convergence rate asymptotic normality

Asymptotic distributions in the projection pursuit based canonical correlation analysis

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Science china.mathematics 2010年第2期53卷 485-498页

作者： JIN Jiao & CUI HengJian Department of Statistics and Financial mathematics, school of mathematical sciences, beijing normal university, laboratory of mathematics and complex systems (beijing normal university), ministry of education, beijing 100875, china 1. Department of Statistics and Financial mathematics School of Mathematical Sciences Beijing Normal University Beijing 100875 China2. Ministry of Education Laboratory of Mathematics and Complex Systems (Beijing Normal University) Beijing 100875 China

In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and we... 详细信息

关键词： asymptotic distribution canonical correlation analysis influence function robust statistics

Quenched moderate deviations principle for random walk in random environment

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Science china.mathematics 2010年第8期53卷 1947-1956页

作者： HONG WenMing 1 & WANG HuaMing 1,2 1 Key laboratory of mathematics and complex systems of ministry of education & school of mathematical sciences,beijing normal university,beijing 100875,china.2 Department of Basic Courses,Business College,beijing Union university,beijing 100025,china 1. Key laboratory of mathematics and complex systems of ministry of education & school of mathematical sciences Beijing Normal University Beijing 100875 China2. Department of Basic Courses Business College Beijing Union University Beijing 100025 China

We derive a quenched moderate deviations principle for the one-dimensional nearest random walk in random environment,where the environment is assumed to be stationary and *** approach is based on hitting time decompos... 详细信息

关键词： random walk in random environment moderate deviations principle hitting time

Compactness of the commutators of parabolic singular integrals

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Science china.mathematics 2010年第10期53卷 2633-2648页

作者： CHEN YanPing1 & DING Yong2,3 1Department of mathematics and Mechanics,university of Science and Technology beijing,beijing 100083,china.2school of mathematical Science,beijing normal university,beijing 100875,china.3laboratory of mathematics and complex systems (BNU),ministry of education of china.beijing 100875,china 1. Department of mathematics and Mechanics University of Science and Technology Beijing Beijing 100083 China2. School of Mathematical Science Beijing Normal University Beijing 100875 China3. Laboratory of Mathematics and Complex Systems (BNU) Ministry of Education of China Beijing 100875 China

In this paper,the authors prove that the commutator [b,T] of the parabolic singular integrals is a compact operator on Lp(Rn)(1 < p < ∞) if and only if b ∈ VMO(Rn,ρ).The result is substantial improvement and extens... 详细信息

关键词： parabolic singular integrals commutators compactness BMO VMO

On weak solutions for an image denoising-deblurring model

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Applied mathematics(A Journal of Chinese Universities) 2009年第3期24卷 269-281页

作者： HUANG Hai-yang JIA Chun-yan HUAN Zhong-dan school of mathematical sciences,beijing normal university laboratory of mathematics and complexsystems,ministry of education,beijing 100875,china school of mathematical sciences Beijing Normal University Beijing China laboratory of mathematics and complex systems Ministry of Education Beijing 100875 China

A new denoising-deblurring model in image restoration is proposed,in which the regularization term carries out anisotropic diffusion on the edges and isotropic diffusion on the regular *** existence and uniqueness of weak solutions for this model are proved,and the numerical model is also *** with the TV diffusion,this model preferably reduces the staircase appearing in the restored images.

关键词： image restoration deblurring-denoising integro-differential equation weak solution