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LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

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Acta Mathematica Scientia 2011年第1期31卷 344-352页

作者：刘莉万成高冯艳钦 school of mathematics and statistics Wuhan University school of Mathmatics and Computer Science Hubei University

In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.

关键词： Large deviation moderate deviation negative dependence non-identical distribution

Assessment and improvement of autocorrelation performance of chaotic sequences using a phase space method

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Science china(Information Sciences) 2011年第12期54卷 2667-2679页

作者： CHEN Bin school of Software and Communication Engineering, JiangXi university of finance and Economy, Nanchang 330032, china 1. school of Software and Communication Engineering JiangXi University of Finance and Economy Nanchang 330032 China

Chaotic sequences have been widely used as pseudorandom sequences. However, how to judge whether their autocorrelation performance is good remains a problem because we have no simple method for assessing and improving the autocorrelation performance. Using a phase space method, we have discovered that the autocorrelation performance of a chaotic sequence is determined by whether its phase space trajectory is axis symmetrical, and have deduced theorems to describe and solve these problems. This paper presents a simple yet effective method to assess and improve the autocorrelation performance of chaotic sequences. Several simulations are presented to validate the theorems and method.

关键词： chaos autocorrelation pseudorandom sequences phase space

An efficient algorithm for finding the largest chain graph according to a given chain graph

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同方期刊数据库

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Science china mathematics 2005年第11期48卷 1517-1530页

作者： LIU Baijun,ZHENG Zhongguo & ZHAO Hui school of Mathematical Sciences, Peking university, Beijing 100871, china Department of statistics, Central china Normal university, Wuhan 4.0079, china 1. school of Mathematical Sciences Peking University 100871 Beijing China 2. Department of statistics Central China Normal University 430079 Wuhan China

Chain graph (CG) is a general model of graphical Markov models. Some different chain graphs may describe the same conditional independence structure, then we say that these CGs are Markov equivalent. In 1990 Frydenberg showed that every class of Markov equivalent CGs has a CG which is called the largest chain graph with the greatest number of lines. This paper presents an efficient algorithm for finding the largest chain graph of the corresponding Markov equivalent class of a given CG. The computational complexity of the algorithm is O(n3). It is more efficient than the complexity O(n!) of the present algorithms. Also a more intuitive graphical characterization of the largest chain graph is provided based on the algorithm in this paper.

关键词： graphical Markov model,chain graph,largest chain graph,protected arrows,efficient algorithm

Wavelet estimation of the diffusion coefficient in time dependent diffusion models

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Science china mathematics 2007年第11期50卷 1597-1610页

作者： Ping CHEN~(1,2+) Jin-de WANG~1 1 Department of mathematics,Nanjing university,Nanjing 210093,china 2 school of Science,Nanjing university of Science and Technology,Nanjing 210094.china Department of mathematics Nanjing University Nanjing 210093 China school of Science Nanjing University of Science Technology Nanjing 210094 China

The estimation problem for diffusion coefficients in diffusion processes has been studied in many papers,where the diffusion coefficient function is assumed to be a 1-dimensional bounded Lipschitzian function of the state or the time *** is no previous work for the nonparametric estimation of time-dependent diffusion models where the diffusion coefficient depends on both the state and the *** paper introduces and studies a wavelet estimation of the time-dependent diffusion coefficient under a more general assumption that the diffusion coefficient is a linear growth Lipschitz *** the properties of martingale,we translate the problems in diffusion into the nonparametric regression setting and give the Lr convergence rate.A strong consistency of the estimate is *** this result one can estimate the time-dependent diffusion coefficient using the same structure of the wavelet estimators under any equivalent probability *** example,in finance,the wavelet estimator is strongly consistent under the market probability measure as well as the risk neutral probability measure.

关键词： wavelet estimation time-dependent diffusion coefficient linear growth condition strong consistency

On the Markov equivalence of maximal ancestral graphs

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Science china mathematics 2005年第4期48卷 548-562页

作者： ZHAO Hui, ZHENG Zhongguo & LIU Baijun school of Mathematical Sciences, Peking university, Beijing 100871, china Department of statistics, Central china Normal university, Wuhan 4.0079, china 1. school of Mathematical Sciences Peking University 100871 Beijing China

Necessary and sufficient conditions for a maximal ancestral graph (MAnG)to be Markov equivalent to another MAnG and to a DAG are provided respectively. Also a polynomial-time algorithm for converting a MAnG into its e... 详细信息

关键词： maximal ancestral graph, Markov equivalence, minimal collider path, m-separation.

Kernel-based Nonlinear Fit with Total Least Square（TLS） Method

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Kernel-based Nonlinear Fit with Total Least Square（TLS） Me...

Large deviations for Glauber dynamics of continuous gas

第二十六届中国控制会议

作者： Hu Guanghua,Fu Guanghui school of mathematics and statistics,yunnan {4.,Kunming 650091,P.R.china

In this paper,on the basis of linear fit in the total least square（TLS）method sense,we proposed a method of nonlinear fit in the TLS method sense via kernel ***,by using an appropriate kernel function,the problems of nonlinear fit can be transformed to the problems of linear fit without paying the computational penalty and without the precondition that the fitting function type of the data points is *** experimental results show that the algorithm presented in this paper is available.

关键词： Linear fit Nonlinear fit Kernel method Total Least Square(TLS)method

来源： cnki会议评论

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cnki会议

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Science china mathematics 2008年第5期51卷 973-986页

作者： SONG QiongXia~(1,2) 1 school of Mathematical Sciences,Wuhan university,Wuhan 4.0072,china 2 Department of statistics and Probability,Michigan State university,East Lansing,MI4.824.USA school of Mathematical Sciences Wuhan University Wuhan 430072 China Department of statistics Probability Michigan State University East Lansing MI48824 USA

This paper is devoted to the large deviation principles of the Glauber-type dynamics of finite or infinite volume continuous particle systems. We prove that the level-2 empirical process satisfies the large deviation principles in the weak convergence topology, while it does not satisfy the large deviation principles in the τ-topology.

关键词： Gibbs measures Glauber dynamics empirical processes large deviation principles 60J25 60F10 82B21 82C21

Statistical Inference for Simple Tree Order in the Means of Stochastic Order on Stratified Contingency Tables

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Wuhan university Journal of Natural Sciences 2010年第2期15卷 93-98页

作者： YAN Guoyi1,2, CHEN Jingjing3 1.school of mathematics and statistics, Wuhan university, Wuhan 4.0072, Hubei, {4. 2. school of Sciences, Wuhan Institute of Technology, Wuhan 4.0074. Hubei, {4. 3. school of Sciences, Wuhan university of Science and Technology, Wuhan 4.0081, Hubei, {4. school of mathematics and statistics Wuhan University Wuhan China school of Sciences Wuhan Institute of Technology Wuhan China school of Sciences Wuhan University of Science and Technology Wuhan China

In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula- tions are in simple tree order. We provide an asymptotic represen- tation of the order-restricted maximum likelihood estimate of the unknown parameters. The resulting estimators are proven to be ~n-consistent and asymptotically normal under appropriate conditions. A chi-squared test method is used for this hypothesis test problem. A real data set is applied to illustrate our theoretical result.

关键词： simple tree order chi-squared test asymptotic representation asymptotic distribution

Latent ancestral graph of structure vector autoregressive models

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Journal of Systems Engineering and Electronics 2010年第2期21卷 233-238页

作者： Wei Gao1,2and Zheng Tian2,3 1.school of statistics,Xi’an university of finance&Economics,Xi’an 710061,P.R.{4. 2.Department of Applied mathematics,Northwestern Polytechnical university,Xi’an 710072,P.R.{4. 3.State Key Laboratory of Remote Sensing Science,Institute of Remote Sensing Applications,Chinese Academy of Sciences,Beijing 100101,P.R.{4. school of statistics Xi'an University of Finance & EconomicsXi'an 710061P.R.China Department of Applied mathematics Northwestern Polytechnical UniversityXi'an 710072P.R.China Department of Applied mathematics Northwestern Polytechnical UniversityXi'an 710072P.R.China State Key Laboratory of Remote Sensing Science Institute of Remote Sensing ApplicationsChinese Academy of SciencesBeijing 100101P.R.China

A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive （VAR） model affected by latent variables is proposed. The graphs are mixed graphs with possibly two kind of edges, namely directed and bidirected edges. The vertex set denotes random variables at dif- ferent times. In Gaussian case, the latent ancestral graph leads to a simple parameterization model. A modified iterative conditional fitting algorithm is presented to obtain maximum likelihood esti- mation of the parameters. Furthermore, a log-likelihood criterion is used to select the most appropriate models. Simulations are performed using illustrative examples and results are provided to demonstrate the validity of the methods.

关键词： multivariate time series latent ancestral graph itera- tive conditional fitting.