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Orthogonal arrays obtained by generalized difference matrices with g levels

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Science China Mathematics 2011年第1期54卷 133-143页

作者： ZHANG YingShan LI WeiGuo MAO ShiSong zheng zhongguo School of Finance and Statistics East China Normal University Shanghai 200241 China School of Sciences Beijing University of Aeronautics and Astronautics Beijing 100083 China Lab of Mathematics and Its Application Peking University Beijing 100871 China

Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction for many mixed orthogonal arrays. But there are also orthogonal arrays which cannot be obtained by the usual difference matrices, such as mixed orthogonal arrays of run size 60. In order to construct these mixed orthogonal arrays, a class of special so-called generalized difference matrices were discovered by Zhang (1989,1990,1993,2006) from the orthogonal decompositions of projection matrices. In this article, an interesting equivalent relationship between orthogonal arrays and the generalized difference matrices is presented and proved. As an application, a lot of new orthogonal arrays of run size 60 have been constructed.

关键词： mixed-level orthogonal arrays generalized difference matrices projection matrices permutation matrices

Random Weighting Method

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数学进展 1989年第1期 44-54页

作者： zheng zhongguo(Department of Probability and Statistics, Peking University)

*** Since Efron's weIl known paper apPeared in 1979,there hasbeen enormous work8 0n resampling *** all these techniques,bootstraP isconceptually the simplest and the most attractiye one. But for setting confidenceinterval, the confidenee level of the interval set by the boot8trap method, especi-ally for small sample size, is less than what we 0riginaIly exPected. The purPoseof this paPer is to discuss an alternatiVe method,the random weighting method,whichwas originally suggested by *** study shows that the randomweighting method can reduce the level error of the confidence interVal for themeasure model. In section 2, the assymptotical behaVior of random weightingmethod for measure model is discussed. In 8ection 3, the random weighting me—

关键词： Random Weighting Method

A SIMPLE METHOD FOR CONSTRUCTING ORTHOGONAL ARRAYS BY THE KRONECKER SUM

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Journal of Systems Science & Complexity 2006年第2期19卷 266-273页

作者： Yingshan ZHANG Weiguo LI Shisong MAO zhongguo zheng Department of Statistics East China Normal University Shanghai 200062 China Lab of Mathematics and Its Application Peking University Beijing 100871 China School of Sciences Beijing University of Aeronautics and Astronautics Beijing 100083 China

In this article, we propose a new general approach to constructing asymmetrical orthogonal arrays, namely the Kronecker sum. It is interesting since a lot of new mixed-level orthogonal arrays can be obtained by this m... 详细信息

关键词： Difference matrices Kronecker sum mixed-level orthogonal arrays permutation matrices projection matrices.

OPTIMAL RATE OF CONVERGENCE FOR ESTIMATORS IN THE NONPARAMETRIC MEDIAN MODEL

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Systems Science and Mathematical Sciences 1992年第3期5卷 239-250页

作者： zheng zhongguo (Peking University,Beijing 100871,China)

Let(Y,X)be a random vector with its value in R^1×R^d,d(?)***(?)be the collection of real valued functions θ(x) on R^d which is p times differ-entiable at x=0 and p-1 times differentiable on an open neighborhood U ofthe origin of R^*** conditional distribution of Y is assumed to be of the formof f(y|x,θ(x))dy where θ(x)∈(?)is called the parameter of the family.(Y,X)iscalled a nonparametric median model if furthermore the conditional median of Ygiven X=x is θ(x).In this paper,the optimal rate of convergence for estimatorsof T(θ)=θ(0)is *** certain conditions,it is proved that for thenonparametric median model the optimal rate of convergence is r=p/(2p+d).A sequence of estimators,which is asymptotically normal with the optimal rate ofcovergence,is constructed.

关键词： Optimal rate of convergence nonparametric median model

VIRTUAL SYSTEM METHOD FOR SYSTEM TREE

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Chinese Annals of Mathematics,Series B 1995年第4期16卷 509-518页

作者： zheng zhongguo (Department of Probability and Statistics, Beijing University) Be1Jing 100871, China.) 北京大学概率统计系北京

A machine, or other type of 'system' , can often be divided into several subsystems (components)and these subsystems again can be divided into sevreral subsystems (second generation). This process forms a system tree. To assess the reliability of the machine based on data from the trials of components of the machine, virtual system method is employed. It is proved in the paper that the lower confident limit of the reliability of the machine set by the virtual system method is level consistent and asymptotically optimal while the one set by Lindstrom-Maddens method is not.

关键词： Lower confidence limit Reliability Virtual system method System tree

IMPROVEMENT ON THE TEST IN THE EXPONENTIAL FAMILY

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Systems Science and Mathematical Sciences 1993年第2期6卷 137-144页

作者： zheng zhongguo Peking University, Beijing 100871, China 北京大学北京

Let x1,…, xn be the life spans of n items. Suppose that we start the experi-ment at the time t=0 for all the items simultaneuously aud stop the experiment at the timet=r, where r is a stopping time. The observed data set is Zn=(x1,…, xk, r（x）),where xi（i=1,…, n） is the order statistic of xi, i=1,…, n and k=k（x） is the num-ber of the observed data. Suppose that the distribution family of xi, i=1,…, n is *** with life expectation θ>0. For testing the hypothesis H0: θ≤θ0 againstH1: θ>θ0, we use the total time of experiment Sr=sub from i=1 to k xi +（n-k）r （x） as the teststatistic. We reject H0 as large value of Sr is observed. In this paper for a given stoppingtime r we construct a stopping time ro so that the resulting test is a best improvement ofthe one, which is based on r, in the sense that the power functions of the two tests are thesame but the test based on r0 is the one which has the minimnm total experiment time.

关键词： Exponential distribution best improvement of test

Random Weighting T-Statistics in Linear Regression Models

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Acta Mathematica Sinica,English Series 1995年第2期11卷 188-199页

作者： Shi Jian zheng zhongguo Department of Probability and Statistics Peking University Beijing, 100871 China Peking University

In this paper, we have constructed a random weighting statistic to approximate the distribution of studentized least square estimator in a linear regression model with ideal accuracy o(n-1/2). Thus, we have provided a... 详细信息

关键词： Random Weighting T-Statistics in Linear Regression Models

Choice of Optimal Trimming Proportion by the Random Weighting Method

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Acta Mathematica Sinica,English Series 1996年第3期12卷 326-336页

作者： Shi Jian zheng zhongguo, Department of Probability and Statistics Peking University Beijing, 100871 China 北京大学概率统计系北京

In this paper, a strongly consistent estimation of the optimal trimming proportion in trimmed mean is found by the random weighting method. In addition, using the same method a strongly consistent estimation for the d... 详细信息

关键词： Trimmed mean Trimming proportion Bootstrap Random weighting

MUCLTIVARIATE RESISTANT REGRESSION SPLINES FOR ESTIMATING MULTIVARIATE FUNCTIONS FROM NOISY DATA

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Systems Science and Mathematical Sciences 1997年第3期10卷 217-224页

作者： SHI Peide zheng zhongguo(Department of Probability and Statistics, Peking University, Beijing 100871, China)

The multivariate resistant regression spline (MURRS) method for estimatingan underlying smooth J-variate function by using noisy data is based on approximatingit with tensor products of B-splines and minimizing a sum of the ρ-functions of the residuals to obtain a robust estimator of the regression function, where the spline knots areautomatically chosen through a parallel of information criterion. When the knots are deterministically given, it is proved that the MURRS estimator achieves the optimal globalconvergence rates established by Stone under some mild conditions. Examples are givento illustrate the utility of the proposed methodology. Usually, only a few tensor productsof B-splines are enough to fit even complicated functions.

关键词： Regression spline M-estimator nonparametric regression tensor products of B-splines.