1997年, 第10卷, 第3期　刊出日期：1997-07-15

  

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  ASYMPTOTIC PROPERTIES OF MLE IN EXPONENTIAL FAMILY NONLINEAR MODELS

  ZHU Zhongyi;WEI Bocheng

  Journal of Systems Science and Complexity. 1997, 10(3): 193-201.

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  In this paper, a necessary condition for the existence of any weakly consistent estimator is presented in exponential family nonlinear models. Then we give one more necessary condition for a consistent estimator in generalized linear models. Under mild regularity conditions, the existence, the strong consistency and the asymptotic normality of MLE are proved in exponential family nonlinear models. Our results may be regardedas a further work of [1] in generalized linear models.
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  A TEST FOR SPHERICITY OF ERRORS IN LINEAR MODELS

  WANG Songgui;YANG Zhenhai

  Journal of Systems Science and Complexity. 1997, 10(3): 202-207.

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  For a general linear model, spherical distributions are often considered when errors do not have normal distribution. Several authors[1-3] studied the least squares and James-Stein estimations for a linear model whose errors follow multivariate t or more general spherical distributions. In this paper the test problem for sphericity of errors isconsidered. We propose an exact test for the sphericity by using the conditional probability integral transformation and another transformation. As an important special case, the corresponding test statistics for multivariate t distribution are obtained.
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  ON THE CONDITION FOR CONSISTENCY OF RESAMPLING ESTIMATORS OF VARIANCE OF TRIMMED L-STATISTICS

  SHI Jian;ZHENG Zhongguo

  Journal of Systems Science and Complexity. 1997, 10(3): 208-216.

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  In this paper, a counter-example is presented to show that conditions given by[1] and [2] are not enough to guarantee the consistency of resampling estimators of varianceof trimmed L-statistics. To this end, a rather weak but sufficient condition is proposedto ensure the strong consistency. Lastly, a declaration in [3] on the generalization of amodified resampling procedure is found to be invalid.
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  MUCLTIVARIATE RESISTANT REGRESSION SPLINES FOR ESTIMATING MULTIVARIATE FUNCTIONS FROM NOISY DATA

  SHI Peide;ZHENG Zhongguo

  Journal of Systems Science and Complexity. 1997, 10(3): 217-224.

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  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.
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  ASYMPTOTIC NORMALITY OF M-ESTIMATES IN THE EV MODEL

  CUI Hengjian

  Journal of Systems Science and Complexity. 1997, 10(3): 225-236.

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  The M-estimate of parameters in the errors-in-variables (EV) model Y =x^τβ_0+∈, X =x+u ((∈,u^τ)^τ is a (p+1)-dimensional spherical error, Coy[(∈, u^τ)^τ] =σ^2I_{p+1})being considered. The M-estimate \bar{β}_n of β_0 under a general ρ(·) function and the estimateof \bar{σ}_n^2 are given, the strong consistency and asymptotic normality of \bar{β}_n as well as \bar{σ}_n^2 are obtained. The conditions for the ρ(·) function in this paper are similar to that of linearexpression of M-estimates in the linear regression model.
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  QUEUEING NETWORK MODELING AND ANALYSIS IN THE DESIGN AND EVALUATION OF SEAPORT SYSTEMS

  CHAO Xiuli;GU Jifa;HU Pingxian

  Journal of Systems Science and Complexity. 1997, 10(3): 237-252.

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  In this paper we apply networks of queues in the design and analysis of aseaport system. There are two types of ports, the deep water port and shallow waterport. The steamships arrive via the Pacific ocean according to a random process, andcan only enter the deep water port (due to the size of the ships). The finite capacity of the port, often results in long delays which is undsirable. To reduce this congestion problem, ports authorities are considering constructing a platform (or dock) in a deepwater area on which some steamships can be first downloaded, and then the goods onthe platform are delivered and downloaded on the shallow water port by many small-sizeboats. This sytstem is modeled as a network of queues with finite buffers and blocking. We develop approximation methodology for analyzing queue delays, and apply it, in thedesign and optimization of the port systems. The algorithm is proved to be efficient, and its effectiveness is shown by both numerical results and simulation analysis.
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  A MUCLTI-PARAMETER SPLITTING EXTRAPOLATION AND A PARALLEL ALGORITHM

  ZHOU Aihui;Liem Chin-ho;Shih Tsi-min;LU Tao

  Journal of Systems Science and Complexity. 1997, 10(3): 253-260.

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  The finite element solutions of elliptic equations are shown to have a multiparameter asymptotic error expansion. Based on this expansion and a multi-parameter splitting extrapolation technique, a parallel algorithm for solving multi-dimensional equations with high order accuracy is introduced.
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  SOME STABILITY THEOREMS FOR DIFFERENCE EQUATIONS WITH TIME DELAY

  CHEN Jufang

  Journal of Systems Science and Complexity. 1997, 10(3): 261-266.

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  Here several theorems are established to discuss uniform stability and uniform asymptotical stability of zero solution for difference equations with time delay. These theorems extend Razumikhin Method from functional differential equations to time delay difference equations.
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  PATH EXTENSIBILITY OF CONNECTED, LOCALLY 2-CONNECTED K_{1,3}-FREE GRAPHS

  WANG Jianglu;ZHU Yongjin

  Journal of Systems Science and Complexity. 1997, 10(3): 267-274.

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  In this paper, we prove that every connected, locally 2-connected claw-freegraph is path extendable.
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  ON THE BOUNDARY STABILIZATION OF WAVE EQUATION WITH VARIABLE COEFFICIENT

  ZHANG Weitao;FENG Dexing

  Journal of Systems Science and Complexity. 1997, 10(3): 275-281.

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  This paper is concerned with the stabilization problem of wave equation with variable coefficient under boundary feedback control. It is shown that the energy of the system decays exponentially if the feedback parameters are chosen in some domain.
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  METHODS FOR IMPROVING APPROXIMATE ACCURACY FOR HYPERBOLIC INTEGRODIFFERENTIAL EQUATIONS

  LIN Qun;ZHANG Shuhua;YAN Ningning

  Journal of Systems Science and Complexity. 1997, 10(3): 282-288.

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  In this paper we study the higher accuracy methods-the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of hyperbolic integrodifferential equations. The global extrapolation and the correction approximations of third order, rather than the pointwise extrapolation results, are derived.