Exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays

This paper studies the problems of global exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential stability in the mean square for the reaction-diffusion high-order neural networks are established, which are easily verifiable and have a wider adaptive. An example is also discussed to illustrate our results.     

Improved results for stochastic stabilization of a class of discrete-time singular Markovian jump systems with time-varying delay

In this paper, the problem of stochastic stabilization for a class of discrete-time singular Markovian jump systems with time-varying delay is investigated. By using the Lyapunov functional method and delay decomposition approach, improved delay-dependent sufficient conditions are presented, which guarantee the considered systems to be regular, causal and stochastically stabilizable. Finally, some numerical examples are provided to illustrate the effectiveness of the obtained methods.     

Detecting changes in the ar parameters of a nonstationary arma process

We present a method for detecting changes in the AR parameters of an ARMA process with arbitrarily time varying MA parameters. Assuming that a collection of observations and a set of nominal time invariant AR parameters are given, we test if the observations are generated by the nominal AR parameters or by a different set of time invariant AR parameters. The detection method is derived by using a local asymptotic approach and it is based on an estimation procedure which was shown to be consistent under nonstationarities.     

Stability analysis of the differential genetic regulatory networks model with time-varying delays and Markovian jumping parameters

In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov–Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results.     

L2 − L∞ filtering for Markovian jump systems with time-varying delays and partly unknown transition probabilities

This paper considers the L₂ − L_∞ filtering problem for Markovian jump systems. The systems under consideration involve time-varying delays, disturbance signal and partly unknown transition probabilities. The aim of this paper is to design a filter, which is suitable for exactly known and partly unknown transition probabilities, such that the filtering error system is stochastically stable and a prescribed L₂ − L_∞ disturbance attenuation level is guaranteed. By using the Lyapunov-Krasovskii functional, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of filter design for Markovian jump systems with partly unknown transition probabilities.     

Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.     

On the quadratic estimation of covariance matrices in multivariate linear models

This paper investigates the estimation of covariance matrices in multivariate mixed models. Some sufficient conditions are derived for a multivariate quadratic form and a linear combination of multivariate quadratic forms to be the BQUE (quadratic unbiased and severally minimum varianced) estimators of its expectations.     

Jackknifing in partially linear regression models with serially correlated errors

In this paper jackknifing technique is examined for functions of the parametric component in a partially linear regression model with serially correlated errors. By deleting partial residuals a jackknife-type estimator is proposed. It is shown that the jackknife-type estimator and the usual semiparametric least-squares estimator (SLSE) are asymptotically equivalent. However, simulation shows that the former has smaller biases than the latter when the sample size is small or moderate. Moreover, since the errors are correlated, both the Tukey type and the delta type jackknife asymptotic variance estimators are not consistent. By introducing cross-product terms, a consistent estimator of the jackknife asymptotic variance is constructed and shown to be robust against heterogeneity of the error variances. In addition, simulation results show that confidence interval estimation based on the proposed jackknife estimator has better coverage probability than that based on the SLSE, even though the latter uses the information of the error structure, while the former does not.     

Consistency and asymptotic normality of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models with random regressors

This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） with random regressors. The asymptotic results of generalized linear models （GLM） with random regressors are generalized to QLNM with random regressors.     

Testing hypotheses on the “drift” of parameters in ARMA and ARCH models

For an ARMA model, we test the hypothesis that the coefficients of this model remain constant in time and satisfy the stationarity condition against the alternative that the coefficients change (“drift”) in time. We propose asymptotically distribution free tests for such hypothesis based on sequential residual processes. A similar problem is solved for the ARCH model.      

基于正交表的异方差估计方法改进

关于异方差模型的处理,方差估计及其性质研究是一个有意义的问题。本文针对一种基于正交表估计方差的非参数方法进行了改进。考虑到已有利用正交表的估计方法中,没有充分运用原始数据信息来确定因变量与自变量关系的不足,以及正交表使用中关于容差确定的不合理性,本文在这两方面进行了深入研究。模拟实验与实例分析表明,本文所提出的改进方法与原有正交表方法及HC4方法相比较,是一种更加有效的估计。     

Estimation of the multivariate normal precision and covariance matrices in a star-shape model

In this paper, we introduce the star-shape models, where the precision matrix Ω (the inverse of the covariance matrix) is structured by the special conditional independence. We want to estimate the precision matrix under entropy loss and symmetric loss. We show that the maximal likelihood estimator (MLE) of the precision matrix is biased. Based on the MLE, an unbiased estimate is obtained. We consider a type of Cholesky decomposition of Ω, in the sense that Ω=Ψ′Ψ, where Ψ is a lower triangular matrix with positive diagonal elements. A special group , which is a subgroup of the group consisting all lower triangular matrices, is introduced. General forms of equivariant estimates of the covariance matrix and precision matrix are obtained. The invariant Haar measures on , the reference prior, and the Jeffreys prior of Ψ are also discussed. We also introduce a class of priors of Ψ, which includes all the priors described above. The posterior properties are discussed and the closed forms of Bayesian estimators are derived under either the entropy loss or the symmetric loss. We also show that the best equivariant estimators with respect to is the special case of Bayesian estimators. Consequently, the MLE of the precision matrix is inadmissible under either entropy or symmetric loss. The closed form of risks of equivariant estimators are obtained. Some numerical results are given for illustration. The project is supported by the National Science Foundation grants DMS-9972598, SES-0095919, and SES-0351523, and a grant from Federal Aid in Wildlife Restoration Project W-13-R through Missouri Department of Conservation.     

����״̬������Markov�л����ʱ��ϵͳ�ľ���ָ���ȶ���

考察一类Markov切换时变时滞随机系统的均方指数稳定性. 利用基于Liapunov函数和线性矩阵不等式的方法, 给出了使状态反馈控制系统能克服不确定性和随机干扰, 在均方意义下达到指数稳定的充分条件. 当Markov链遍历所有模态时, 给出了一个独立于Markov链模态集的增益矩阵, 使得状态反馈控制系统均方指数稳定     

多元线性混合模型方差分量矩阵的非负估计

本文研究了带有两个方差分量矩阵的多元线性混合模型方差分量矩阵的估计问题.对于平衡模型,给出了基于谱分解估计的一个方差分量矩阵的非负估计类.对于非平衡模型,给出了方差分量矩阵的广义谱分解估计类,讨论了与ANOVA估计等价的充要条件.同时,在广义谱分解估计的基础上给出了一种非负估计类,并讨论了其优良性.当具有较小二次风险的非负估计不存在时,从估计为非负的概率的角度考虑,将Kelly和Mathew(1993)提出的构造具有更小取负值概率的估计类的方法推广到本文的多元模型下,给出了较谱分解估计相比有更小取负值概率和更小风险的估计类.最后,模拟研究和实例分析表明文中理论结果有很好的表现.     

The superiorities of bayes linear unbiased estimator in multivariate linear models

In this article,the Bayes linear unbiased estimator (BALUE) of parameters is derived for the multivariate linear models.The superiorities of the BALUE over the least square estimator (LSE) is studied in terms of the mean square error matrix (MSEM) criterion and Bayesian Pitman closeness (PC) criterion.     

带有泊松跳跃马尔可夫调制的中立型随机时滞微分方程近似解的依概率收敛

本文在局部Lipschitz条件和一些附加条件下得到了方程的全局解, 而未使用线性增长条件. 另外, 对带有泊松跳跃马尔可夫调制的中立型随机时滞微分方程近似解的收敛性进行了研究, 取代了以往的均方收敛方式, 改为依概率收敛. 从而对现有的一些结果进行了改进.     

Estimation of the Cholesky decomposition in a conditional independent normal model with missing data

We investigate the problem of estimating the Cholesky decomposition in a conditional independent normal model with missing data. Explicit expressions for the maximum likelihood estimators and unbiased estimators are derived. By introducing a special group, we obtain the best equivariant estimators.