Particle-based online estimation of tangent filters with application to parameter estimation in nonlinear state-space models

This paper presents a novel algorithm for efficient online estimation of the filter derivatives in general hidden Markov models. The algorithm, which has a linear computational complexity and very limited memory requirements, is furnished with a number of convergence results, including a central limit theorem with an asymptotic variance that can be shown to be uniformly bounded in time. Using the proposed filter derivative estimator, we design a recursive maximum likelihood algorithm updating the parameters according the gradient of the one-step predictor log-likelihood. The efficiency of this online parameter estimation scheme is illustrated in a simulation study.

     

求解非凸半定规划的一个非线性Lagrange算法及其收敛性分析

本文提出了一个求解非凸半定规划的非线性Lagrange算法,当二阶充分条件以及严格互补条件成立时,证明了这一算法的收敛性定理.收敛结果表明,当惩罚参数小于某个阀值时,算法是局部收敛的;此外,还给出了解的一个依赖于惩罚参数的误差界.     

受控AR模型中参数估计误差的一致有界性分析

本针对系统为受控AR模型，其参数估计采用随机梯度算法时，用鞅收敛定理的推广形式分析了它的收敛性，得到了参数估计误差一致有界的结果．     

双边截断型分布族参数的经验Bayes估计

在Linex损失函数下,讨论一类双边截断型分布族参数的经验Bayes（EB）估计问题,构造了参数的EB估计,在适当的条件下给出了该估计的收敛速度,最后给出例子,说明定理条件的合理性。     

混合模拟退火-进化策略在非线性参数估计中的应用

提出了一种混合模拟退火-进化策略算法应用在非线性参数估计中,方法克服了传统优化方法估计参数精度不高且容易陷入局部极小值等缺点,并且将模拟退火算法和进化策略算法相结合,充分发挥各自算法优点.最后通过给出非线性参数估计算例,结果表明,算法具有参数估计精度较高,收敛速度快,自适应性强,在实际工程中有较大的应用价值.     

On the Convergence of the Brent Method

1.IntroductionItiswellknownthattheBrentmethodforsolvingsystemsofnonlinearequati0nsistosolvethefo1lowingsystem:bymaldnguseoftheorthogonaltriangulaxfaCtoriz8tion.SupP0sethatwehaveanaPprokimationx(k)tox*,asoluti0nof(1.1).Thenthek-thiterativeprocedurecanbedescribedasfollows[1]:wherehk/Oisthedifferencestepcorrespondingtotheindexk(wewilldiscussthechoicesofhkinSecti0n4)-Constructanorthogonalmatrix(usuallybytheHouseholdtransf0rmation)Step4.Ifj相似文献   

双边定时截尾样本下广义逆指数分布形状参数的估计

先给出了广义逆指数分布在双边定时截尾样本下形状参数的最大似然估计,并不能得到估计的显式表达式,但证明了参数在(0,+∞)上最大似然估计是唯一存在的.其次提出用EM算法求出形状参数的估计且该估计具有良好的收敛性,还给出了形状参数的EM估计的渐近方差和近似置信区间;最后通过数值模拟,对形状参数的最大似然估计和EM估计的效果进行了比较,说明了用EM算法求形状参数的估计是可行的,并且模拟效果相对比较好.     

Kohonen neural networks and genetic classification

We discuss the property of a.e. and in mean convergence of the Kohonen algorithm considered as a stochastic process. The various conditions ensuring a.e. convergence are described and the connection with the rate decay of the learning parameter is analyzed. The rate of convergence is discussed for different choices of learning parameters. We prove rigorously that the rate of decay of the learning parameter which is most used in the applications is a sufficient condition for a.e. convergence and we check it numerically. The aim of the paper is also to clarify the state of the art on the convergence property of the algorithm in view of the growing number of applications of the Kohonen neural networks. We apply our theorem and considerations to the case of genetic classification which is a rapidly developing field.     

关于Brown方法的半局部收敛性

在本文中,我们讨论解非线性方程组的Brown方法的半局部收敛性。通过对Brown方法的算法结构作深入的分析,我们将Brown方法变换成带有特殊误差项的近似Newton法,基于这种等价变形,我们建立了Brown方法的半局部收敛定理,从而完善了Brown方法的收敛理论。     

用函数求根法解系统控制问题

提供了一大类系统控制问题的求解路线.当所考察的问题可转化为参数估计时,可以把问题进一步转化为未知回归函数求根(根即待估参数)的问题,而扩展截尾的随机逼近算法是解决这类求根问题的恰当工具.给出了算法的一般收敛定理,它已在一系列系统控制问题中得到应用.以ARMA过程的辨识,Hammerstein系统的适应调节为例,展示了上述求解路线的具体实现,并附有相应的模拟计算实例.这种方法提供的估计是递推的,并且以概率1收敛到真值.     

An innovative fractional order LMS algorithm for power signal parameter estimation

Parameter estimation is an important issue for the quality monitoring and reliability assessment of power systems. In this study, an innovative fractional order least mean square (I-FOLMS) adaptive algorithm is presented for an effective parameter estimation. The I-FOLMS algorithm exploits the fractional gradient in its recursive parameter update mechanism, because its performance can be tuned by means of the fractional order. High values of the fractional order are good for fast convergence, but lead to steady state mis-adjustments. While, low values provide a smooth steady state behavior, but require a compromise in the convergence rate. The effective performance of I-FOLMS is verified and validated through two numerical examples of power signals estimation for different levels of noise variance and values of the fractional orders.     

һ��Coxģ�Ͳ����ľ���Bayes��˫�����

In this paper, the empirical Bayes (EB) two-sided test for parameter of Cox models is investigated under square loss functions. At first by using recursive kernel estimation of probability function the empirical Bayes two-sided test rule is constructed. It proves that the proposed empirical Bayes test rule is asymptotic optimal and convergence rates are obtained under suitable conditions. Finally an example of satisfying theorem conditions is given.     

Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-Burmeister NCP Functions

This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.     

指数分布抽样基本定理及在三参数一般指数分布参数估计中的应用

讨论三参数一般指数分布的参数估计,首先讨论了三参数一般指数分布参数的最大似然估计的求解问题,当其中参数α=1时,应用指数分布抽样基本定理,得到了三参数一般指数分布其它参数的一致最小方差无偏估计;并且由此给出求解三参数一般指数分布参数最大似然估计的迭代方法,得到了三参数一般指数分布参数最大似然估计的近似值,给出了模拟结果以说明迭代方法的收敛性;并以相关文献的观察数据作为样本,得到了三参数一般指数分布的参数估计,从而说明了迭代方法的有效性.     

A preprocessing method for parameter estimation in ordinary differential equations

Parameter estimation for nonlinear differential equations is notoriously difficult because of poor or even no convergence of the nonlinear fit algorithm due to the lack of appropriate initial parameter values. This paper presents a method to gather such initial values by a simple estimation procedure. The method first determines the tangent slope and coordinates for a given solution of the ordinary differential equation (ODE) at randomly selected points in time. With these values the ODE is transformed into a system of equations, which is linear for linear appearance of the parameters in the ODE. For numerically generated data of the Lorenz attractor good estimates are obtained even at large noise levels. The method can be generalized to nonlinear parameter dependency. This case is illustrated using numerical data for a biological example. The typical problems of the method as well as their possible mitigation are discussed. Since a rigorous failure criterion of the method is missing, its results must be checked with a nonlinear fit algorithm. Therefore the method may serve as a preprocessing algorithm for nonlinear parameter fit algorithms. It can improve the convergence of the fit by providing initial parameter estimates close to optimal ones.     

在模型和实际存在差异时的非线性离散时滞系统最优控制算法

研究非线性分布时滞系统最优控制,提出一种基于线性分布时滞模型和二次型性能指标问题的迭代算法,将分布时滞系统化为满足马尔可夫性质的增广状态系统,在模型和实际存在差异的情况下,该算法通过迭代求解分布时滞线性最优控制问题和参数估计问题,获得原问题的最优解。给出该算法收敛于实际最优解的充分条件。     

Further investigation into split common fixed point problem for demicontractive operators

Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point problem of demicontractive mappings in a real Hilbert space. So many authors have used algorithms involving the operator norm for solving split common fixed point problem, but as widely known the computation of these algorithms may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some applications of our result and numerical example at the end of the paper.     

Parametric Inference for imperfectly observed Gibbsian fields

Summary This paper presents a maximum likelihood estimation method for imperfectly observed Gibbsian fields on a finite lattice. This method is an adaptation of the algorithm given in Younes [28]. Presentation of the new algorithm is followed by a theorem about the limit of the second derivative of the likelihood when the lattice increases, which is related to convergence of the method. Some practical remarks about the implementation of the procedure are eventually given.     

A New Two-Model Approach for Optimizing Control of Large-Scale Steady-State Systems

A novel two-model approach for hierarchical system optimizationand parameter estimation of large-scale industrial processesis described which is considerably more efficient and reliablethan previous hierarchical methods for integrated system optimizationand parameter estimation (ISOPE), in the sense that it takesfar fewer changes of controller set points to produce the realoptimum, and its convergent conditions are weaker. Other advantages of this new approach are that the number ofcontroller set-point changes does not depend on the number ofinequality constraints that are tight at the optimum, and itis possible to provide sufficient conditions for global convergencewhich are nearly the same as those of the centralized ISOPEmethod. Optimality of the algorithm is examined, and a proof of theglobal convergence of the algorithm is presented. Computer simulationsare used to demonstrate the behaviour of the algorithm.     

An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory

The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed Itô processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic distribution theory for a generalized multiscale estimator including a feasible central limit theorem with optimal convergence rate on convenient regularity assumptions. The inevitably remaining impact of asynchronous deterministic sampling schemes and noise corruption on the asymptotic distribution is precisely elucidated. A case study for various important examples, several generalizations of the model and an algorithm for the implementation warrant the utility of the estimation method in applications.