OPTIMAL AND ROBUST DETECTION OF MULTIVARIATE OUTLIERS FOR ELLIPTICALLY CONTOURED DISTRIBUTION

The outlier problem for a multivariate elliptically contoured distribu-tion's random sample with mean slippage is defined and the likelihood ratio test ofthe null hypothesis,in which there are no outliers,versus the alternative hypothesis,in which some outliers are present,is derived.We show that the testing problemis invariant under a group of affine transformations and obtain the maximal in-variance which is equivalent to the likelihood ratio testing statistic.Furthermore,the non-null and null density distribution functions of the likelihood ratio testingstatistic are derived.We find that the null density distribution function of thetesting statistic is robust and the density distribution function is a monotonicallikelihood ratio function of the maximal invariance.Therefore,the likelihood ratiotest is a uniformly most powerful invariant test among the group of affine transfor-mations.In the last section,we give an example of detecting multivariate outliersin elliptically contoured distribution.     

OUTLIERS AND INFLUENTIAL OBSERVATIONS IN A RIDGE MEAN SHIFT REGRESSION

ＯＵＴＬＩＥＲＳＡＮＤＩＮＦＬＵＥＮＴＩＡＬＯＢＳＥＲＶＡＴＩＯＮＳＩＮＡＲＩＤＧＥＭＥＡＮＳＨＩＦＴＲＥＧＲＥＳＳＩＯＮＰＡＮＪｉａｎｘｉｎ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＹｕｎｎａｎＰｒｏｖｉｎｃｅ，Ｋｕｎｍｉｎｇ６...     

PREDICTING CHAOTIC TIME SERIES WITH IMPROVED LOCAL APPROXIMATIONS

In this paper, new approaches for chaotic time series prediction are introduced. We first summarize and evaluate the existing local prediction models, then propose optimization models and new algorithms to modify procedures of local approximations. The modification to the choice of sample sets is given, and the zeroth-order approximation is improved by a linear programming method. Four procedures of first-order approximation are compared, and corresponding modified methods are given. Lastly, the idea of nonlinear feedback to raise predicting accuracy is put forward. In the end, we discuss two important examples, i.e. Lorenz system and Rossler system, and the simulation experiments indicate that the modified algorithms are effective.     

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Yk = x'kβ g(tk) εk, 1 < k < n, where Yk's are responses, xk = (xk1,xk2,..... ,xkp)' and tk ∈T ∪R are fixed design points, β= (β1, β2, ....., βp)' is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εk is a linear process given by εk = ∑j=0∞j(?)ek-j,(?)= 1, where , are i.i.d. random variables. In this paper we establish the asymptotic normality of the least squares estimator of β, a smooth estimator of g(.), and estimators of the autocovariance and autocorrelation functions of the linear process εk.     

TIME SERIES FORECASTING WITH MULTIPLE CANDIDATE MODELS： SELECTING OR COMBINING？

Various mathematical models have been commonly used in time series analysis and forecasting. In these processes, academic researchers and business practitioners often come up against two important problems. One is whether to select an appropriate modeling approach for prediction purposes or to combine these different individual approaches into a single forecast for the different/dissimilar modeling approaches. Another is whether to select the best candidate model for forecasting or to mix the various candidate models with different parameters into a new forecast for the same/similar modeling approaches. In this study, we propose a set of computational procedures to solve the above two issues via two judgmental criteria. Meanwhile, in view of the problems presented in the literature, a novel modeling technique is also proposed to overcome the drawbacks of existing combined forecasting methods. To verify the efficiency and reliability of the proposed procedure and modeling technique, the simulations and real data examples are conducted in this study.The results obtained reveal that the proposed procedure and modeling technique can be used as a feasible solution for time series forecasting with multiple candidate models.     

用CIMOSA和随机PETRI网对CIM系统进行行为建模

利用ＣＩＭＯＳＡ建模框架和建模语言，一个企业的集成模型能够被建立．用过程规则集能够对企业模型进行行为分析．为了进一步对ＣＩＭＯＳＡ企业模型的操作进行分析，本文提出了将ＣＩＭＯＳＡ企业模型转换为等价的随机Ｐｅｔｒｉ网模型的系统方法．这种方法是一种将“ｂｏｔ－ｔｏｍ－ｕｐ”和“ｔｏｐ－ｄｏｗｎ”建模方法混合使用Ｐｅｔｒｉ网综合技术．由这种方法得到的Ｐｅｔｒｉ网模型能够保持初始Ｐｅｔｒｉ网的某些定性结构性质     

THE DIRICHLET PROBLEM AND NEUMANN PROBLEM FOR NONLINEAR PARABOLIC SYSTEMS OF SECOND ORDER EQUATIONS WITH MEASURABLE COEFFICIENTS IN A HIGHER DIMENSIONAL DOMAIN

1 Formulation of Dirichlet Problem and Neumann Problem fOrParabolic SystemsLet O be a bounded domain in Rn and the boundary On E C2. Denote Q = g x I,I =0 < t 5 T, 0 < T < ool 0Q = Sl U S2 is the parabolic boundary where S1 = a x {t = 0} is thebottom and S2 = an x I is the lateral boundary. We consider the nonlinear parabolic systemof second order equationsFh(t, xl ut D.u, D:u) -- Hukt = 0 in Q, k = 1, 2,'',m. (l.l)Under certain conditions, system (1.1) can be reduced to the fOrmw…     

A GENERAL APPROACH BASED ON AUTOCORRELATION TO DETERMINE INPUT VARIABLES OF NEURAL NETWORKS FOR TIME SERIES FORECASTING

Input selection is probably one of the most critical decision issues in neural network designing, because it has a great impact on forecasting performance. Among the many applications of artificial neural networks to finance, time series forecasting is perhaps one of the most challenging issues. Considering the features of neural networks, we propose a general approach called Autocorrelation Criterion (AC) to determine the inputs variables for a neural network. The purpose is to seek optimal lag periods, which are more predictive and less correlated. AC is a data-driven approach in that there is no prior assumption about the models for time series under study. So it has extensive applications and avoids a lengthy experimentation and tinkering in input selection. We apply the approach to the determination of input variables for foreign exchange rate forecasting and conduct comparisons between AC and information-based in-sample model selection criterion. The experiment results show that AC outperforms inf     

用现代时域法设计BTT导弹自动驾驶仪

本文先建立了高性能BTT导弹控制系统和两个横向加速度指令数学模型。由于高性能BTT导弹滚转速率较大,俯仰、偏航通道间存在强动力学耦合,但滚动通道可以近似解耦。然后,用本文给出的模型跟随理论设计俯仰一偏航通道自动驾驶仪,用线性二次型理论设计滚动通道自动驾驶仪。为了满足远程全空域BTT导弹作战要求,自动驾驶仪中的增益是滚转速率和动压头的函数。最后,利用某典型地空导弹动力学模型进行了六自由度数字仿真,计算结果表明设计出的自动驾驶仪对导弹结构参数、气动参数、高度等变化具有良好的鲁棒性,导弹侧滑角、脱靶量很小。     

CATALAN NUMBERS, DYCK LANGUAGE AND TIME SERIES OF ELEMENTARY CELLULAR AUTOMATON OF RULE 56

A new approach to study the evolution complexity of cellular automata is proposed and explained thoroughly by an example of elementary cellular automaton of rule 56. Using the tools of distinct excluded blocks, computational search and symbolic dynamics, the mathematical structure underlying the time series generated from the elementary cellular automaton of rule 56 is analyzed and its complexity is determined, in which the Dyck language and Catalan numbers emerge naturally.     

USING DISPLACED CONE REPRESENTATION IN DEA MODELS FOR NONDOMINATED SOLUTIONSIN MULTIOBJECTIVE PROGRAMMING

1.IlltroductionBowlin,etal.[2]extendedtheearlierworkofBowlinetal.11]aspartofaresponsetowhatseemstobeagrowinginterestintheuseofefficiencydominance--asreflected,forexampleintheworkofLoved[7],TulkensandVandenEeckaut[lo]andtheirassociates.ThefocusinBowlinetal.[2]turnedtotheuseofan11metricasabasisfor(1)measuringtheamountofefficiencydominancethatmightbepresentinanyDecisionMakingUnit(DMU)aswellasfor(2)dealingwithproblemsinvolvedinthepossiblepresenceofslackswithnon-zerovalues,--whichareimportantas…     

THE SPLITTING EXTRAPOLATION FOR FINITEELEMENT METHOD

1.IntroductionDespitethesignificantprogressmadeindigitalcomputersandcomputationalmethodsoaferthelasttwodecades,computationalworkaswellascomputerstoragerequiremelltintheappliedfieldissogreatthatsuper-computersarenotabletoaft'ord.111recentyears)thehotpoilltsincomputationalmathematicsarehowtodevelopanealcomPlltationalmethodwhichwouldfulfilthefollowingrequirelllents;1)ItshouldbeaparallelcomputationalIned]'>(lwhichcan11eimplementedonrnultiprocessorcomputersreqlliringminimalcommunicationanloll!{pro(…     

GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES COOPERATIVE SYSTEM WITH TIME DELAYS

ＧＬＯＢＡＬＡＳＹＭＰＴＯＴＩＣＳＴＡＢＩＬＩＴＹＩＮＮ－ＳＰＥＣＩＥＳＣＯＯＰＥＲＡＴＩＶＥＳＹＳＴＥＭＷＩＴＨＴＩＭＥＤＥＬＡＹＳ￥ＣＵＩＪｉｎｇ＇ａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｕｒｕｍ...     

CLASSICAL TIME DEPENDENT SOLUTION FORNEUTRON TRANSPORT IN A SLAB WITHGENERALIZED BOUNDARY CONDITIONS

1.IntroductionSincethepioneeringworkofLehner,WingandJorgens['3],thetimedependentneutrontransportproblemhasbeentreatedbymanyinvestigators,andtheliteratureonthissubjectisconsiderable.Variousmethods,theCO-semigroupmethodin[2,3],theNeumannseriesexpansionmetho…     

THE RATIONALITY OF THE DISCRETE ORDINATES METHOD FOR TIME DEPENDENT NEUTRON TRANSPORT EQUATION

ＴＨＥＲＡＴＩＯＮＡＬＩＴＹＯＦＴＨＥＤＩＳＣＲＥＴＥＯＲＤＩＮＡＴＥＳＭＥＴＨＯＤＦＯＲＴＩＭＥＤＥＰＥＮＤＥＮＴＮＥＵＴＲＯＮＴＲＡＮＳＰＯＲＴＥＱＵＡＴＩＯＮＬＩＸｕｅｚｈｉ；ＺＨＵＧｕａｎｇｔｉａｎ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉ...     

群体排序一致性的逆序数检验法

利用逆序数概念给出一种检验群体排序一致性的方法，并从理论上论证了该方法的合理性．     

STATISTICAL INFERENCE OF WEIBULL DISTRIBUTION FOR TAMPERED FAILURE RATE MODEL IN PROGRESSIVE STRESS ACCELERATED LIFE TESTING

In this note, the tampered failure rate model is generalized from the step-stress accelerated life testing setting to the progressive stress accelerated life testing for the first time. For the parametric setting where the scale parameter satisfying the equation of the inverse power law is Weibull, maximum likelihood estimation is investigated.     

THE DOMAIN DECOMPOSITION TECHNIQUES FOR THE FINITE ELEMENT PROBABILITY COMPUTATIONAL METHODS

1. IntroductionWe have discussed probability computational methods of finite element methods in [1,2,3,4].Probability computational methods have many advalltages. The advantages are more obviousin three dimensions for finite element problems. In probability model, the time that the particlemoves from one place to the boundary of the domain and is absorbed by the boundary (whichis called the time of running up to the boundary for short) is only dependent on the averagedistance between the start…     

ALMOST PERIODIC SOLUTION FOR A CLASS OF LOTKA-VOLTERRA TYPE N-SPECIES ECOLOGICAL SYSTEMS WITH TIME DELAY

The uniform permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type N-species competitive systems with diffusion and delays are investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and new sufficient conditions are obtained for the global asymptotic stability of the unique positive almost periodic solution of the system.     

A PRECONDITIONER FOR DOMAIN DECOMPOSITION METHODS WITH MORTAR LAGRANGE MULTIPLIERS

In this paper we consider the domain decomposition methods with mortar element Lagrange multipliers to two-dimensional elliptic problems. We shall construct a kind of simple preconditioners for the corresponding interface equation. It will be shown that condition number of the preconditioned interface matrix is almost optimal.