ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR THE PARAMETERS OF MULTI－PARAMETER DISCRETE EXPONENTIAL FAMILY

For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.

HAZARD REGRESSION WITH PENALIZED SPLINE:THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.

Constructing Confidence Regions for Autoregressive-Model Parameters

We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions;Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable;instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.

Stability of stochastic neural networks with Markovian jumping parameters

The global asymptotical stability for a class of stochastic delayed neural networks （SDNNs） with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito＇s differential rule, new delay-dependent stability conditions are derived. All results are expressed in terms of linear matrix inequality （LMI）, and a numerical example is presented to illustrate the correctness and less conservativeness of the proposed method.

Stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks with mixed delays and the Wiener process based on sampled-data control

We investigate the stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks （MJFCNNs） with discrete, unbounded distributed delays, and the Wiener process based on sampled-data control using the linear matrix inequality （LMI） approach. The Lyapunov–Krasovskii functional combined with the input delay approach as well as the free-weighting matrix approach is employed to derive several sufficient criteria in terms of LMIs to ensure that the delayed MJFCNNs with the Wiener process is stochastic asymptotical synchronous. Restrictions （e.g., time derivative is smaller than one） are removed to obtain a proposed sampled-data controller. Finally, a numerical example is provided to demonstrate the reliability of the derived results.

Energy Spectrum for a Short-Range 1/r Singular Potential with a Non-Orbital Barrier Using the Asymptotic Iteration Method

Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

The singularly perturbed boundary value problem for quasilinear third-order ordinary differential equation involving two small parameters has been considered. For the three cases epsilon/mu (2) --> 0(mu --> 0), mu (2)/epsilon --> 0(epsilon --> 0) and epsilon = mu (2), the formal asymptotic solutions are constructed by the method of two steps expansions and the existences of solution are proved by using the differential inequality method. In addition, the uniformly valid estimations of the remainder term are given as well.

Singularly perturbed problem for non-local reaction-diffusion equations involving two small parameters

The problem of two small parameters in ordinary differential equations were extended to that in partial differential equations. The initial boundary problem for the singularly perturbed non-local reaction-diffusion equation was solved. Under suitable conditions, the formal asymptotic solutions were constructed using the method of two-step expansions and the uniform validity of the solutions was proved using the differential inequality.

TECHNICAL STABILITY OF NONLINEAR TIME-VARYING SYSTEMS WITH SMALL PARAMETERS

Technical stability:allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condition, technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method. Explicit criteria of technical stability are established in terms of coefficients of the system under consideration. Conditions under which the technical stability of the system can be derived from its reduced linear time-varying (LTV) system were further examined, as well as a condition for linearization approach to technical stability of general nonlinear systems. Also, a simple algebraic condition of exponential asymptotic stability of LTV systems is presented. Two illustrative examples are given to demonstrate the availability of the presently proposed method.

Asymptotic Formulas of the Solutions and the Trace Formulas for the Polynomial Pencil of the Sturm-Liouville Operators

This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas for the eigenvalues of a simple boundary problem generated in a finite interval by the considered Sturm-Liouville equation.

Confidence Regions with Nuisance Parameters

Consider a distribution with several parameters whose exact values are unknown and need to be estimated using the maximum-likelihood technique. Under a regular case of estimation, it is fairly routine to construct a confidence region for all such parameters, based on the natural logarithm of the corresponding likelihood function. In this article, we investigate the case of doing this for only some of these parameters, assuming that the remaining (so called nuisance) parameters are of no interest to us. This is to be done at a chosen level of confidence, maintaining the usual accuracy of this procedure (resulting in about 1% error for samples of size , and further decreasing with 1/n). We provide a general solution to this problem, demonstrating it by many explicit examples.

类渐近线特性在摄像机标定中的应用研究

针对机器视觉领域内的摄像机标定,本研究首次根据渐近线的特性引入物理意义,对摄像机的内、外参数进行标定。首先使用6×6的圆孔标定板,计算出摄像机的投影矩阵。然后根据极限的定义,当像平面上投影点p(u,v)在v不变,u趋向正无穷时,光心与点p的连线形成类渐近线,该渐进线平行于摄像机坐标系XC轴,在标定时将其作为XC轴。根据这一特性,对得到的投影矩阵进行分解得到摄像机内、外参数。最后依据所提出的方法进行标定实验,得到摄像机投影矩阵以及相应的内、外参数。结果表明,根据该方法得到的标定数据反求特征点的投影坐标,与实际对应的图像特征点存在较小误差;并且得到的内、外参数与Faugeras标定法得到的结果误差较小,符合工程实际的精度要求。

Precision motion control for electro-hydraulic axis systems under unknown time-variant parameters and disturbances

This article focuses on asymptotic precision motion control for electro-hydraulic axis systems under unknown time-variant parameters,mismatched and matched disturbances.Different from the traditional adaptive results that are applied to dispose of unknown constant parameters only,the unique feature is that an adaptive-gain nonlinear term is introduced into the control design to handle unknown time-variant parameters.Concurrently both mismatched and matched disturbances existing in electro-hydraulic axis systems can also be addressed in this way.With skillful integration of the backstepping technique and the adaptive control,a synthesized controller framework is successfully developed for electro-hydraulic axis systems,in which the coupled interaction between parameter estimation and disturbance estimation is avoided.Accordingly,this designed controller has the capacity of low-computation costs and simpler parameter tuning when compared to the other ones that integrate the adaptive control and observer/estimator-based technique to dividually handle parameter uncertainties and disturbances.Also,a nonlinear filter is designed to eliminate the“explosion of complexity”issue existing in the classical back-stepping technique.The stability analysis uncovers that all the closed-loop signals are bounded and the asymptotic tracking performance is also assured.Finally,contrastive experiment results validate the superiority of the developed method as well.

PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS

We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator （LSE） when a small dispersion parameter ε→0 and n →∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.

One-sided empirical Bayes test for location parameter in Gamma distribution

In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.

ASYMPTOTIC BEHAVIOR OF UNSTABLE ARMA PROCESSES WITH APPLICATION TO LEAST SQUARES ESTIMATES OF THEIR PARAMETERS

A time series x(t), t≥1, is said to be an unstable ARMA process if x(t) satisfies an unstableARMA model such asx(t)=a_1x(t-1)+a_2x(t-2)+…+a_8x(t-s)+w(t)where w(t) is a stationary ARMA process; and the characteristic polynomial A(z)=1-a_1z-a_2z^2-…-a_3z^3 has all roots on the unit circle. Asymptotic behavior of sum form 1 to n (x^2(t)) will be studied by showing somerates of divergence of sum form 1 to n (x^2(t)). This kind of properties Will be used for getting the rates of convergenceof least squares estimates of parameters a_1, a_2,…, a_?

Kolmogorov-Smirnov APF Test for Inhomogeneous Poisson Processes with Shift Parameter

In this article, we study the Kolmogorov-Smirnov type goodness-of-fit test for the inhomogeneous Poisson process with the unknown translation parameter as multidimensional parameter. The basic hypothesis and the alternative are composite and carry to the intensity measure of inhomogeneous Poisson process and the intensity function is regular. For this model of shift parameter, we propose test which is asymptotically partially distribution free and consistent. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameter.

A Note on the Continuity of the Generalized Curve Subdivision Scheme with Tension Parameter

A generalized non-stationary curve subdivision （GNS for short） scheme of arbitrary order k≥3 with a parameter has been proposed by Fang et al. in the paper （Fang Mei-e et al., CAGD, 2010（27）： 720-733）. It has been proved that the proposed scheme of order k generates C^k-2 continuous curves for k≥4. But the proof of the smoothness in this paper is uncompleted. Moreover, the Cl-continuity of the third order scheme has not been discussed. For this reason, in this paper, we provide a full corrected proof of the smoothness of the GNS scheme of order k for k≥3.

A NEW ESTIMATE OF SHAPE PARAMETER IN THE FAMILY OF GAMMA DISTRIBUTION

In this paper, a new estimator of the shape parameter in the family of Gamma distribution is constructed by using the moment idea, and it is proved that this estimator is strongly consistent and asymptotically normal.

Empirical Bayes Test for Two-parameter Exponential Distribution under Type-Ⅱ Censored Samples

The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.