Higher Moments and Prediction‐Based Estimation for the COGARCH(1,1) Model

COGARCH models are continuous time versions of the well‐known GARCH models of financial returns. The first aim of this paper is to show how the method of prediction‐based estimating functions can be applied to draw statistical inference from observations of a COGARCH(1,1) model if the higher‐order structure of the process is clarified. A second aim of the paper is to provide recursive expressions for the joint moments of any fixed order of the process. Asymptotic results are given, and a simulation study shows that the method of prediction‐based estimating function outperforms the other available estimation methods.     

On the Simultaneous Estimation of Scale Parameters

This note is an extension of Das Gupta's results (1986) on the estimation of multiparameter gamma distribution. Consider p (p ? 2) independent positive random variables with possibly different scale-parameter densities. For the estimation of the powers of the scale parameters it is shown that the “best multiple estimator” is inadmissible with respect to a large class of weighted quadratic loss functions.     

Empirical bayes rules for selecting good populations

A problem of selecting populations better than a control is considered. When the populations are uniformly distributed, empirical Bayes rules are derived for a linear loss function for both the known control parameter and the unknown control parameter cases. When the priors are assumed to have bounded supports, empirical Bayes rules for selecting good populations are derived for distributions with truncation parameters (i.e. the form of the pdf is f(x|θ)= p_i(x)c_i(θ)I_{(0, θ)}(x)). Monte Carlo studies are carried out which determine the minimum sample sizes needed to make the relative errors less than ε for given ε-values.     

Minimizing the expected sample range

Let X_i be i.i.d. random variables with finite expectations, and θ_i arbitrary constants, i=1,…,n. Y_i=X_i+θ_i. The expected range of the Y's is R_n(θ₁,…,θ_n)=E(maxY_i-minY_i. It is shown that the expected range is minimized if and only if θ₁=?=θ_n. In the case where the X_i are independently and symmetrically distributed around the same constant, but not identically distributed, it is shown that θ₁=?=θ_n are not necessarily the only (θ₁,...,θ_n) minimizing R_n. Some lemmas which are applicable to more general problems of minimizing R_n are also given.     

Na_2ZnCl_4·3H_2O:Mn~(2+)晶体ZFS参量单轴压力效应的理论解释

利用对角化完全能量矩阵的方法,借助于文献〔5〕提出的新模型,计算了Na_2ZnCl_4·3H_2O:Mn~(2+)晶体零场分裂(zero—field splitting,简称ZFS)参量及其单轴压力行为,计算值与实验值十分吻合。     

L_2［0，T］空间上的三个最小范数问题及其应用

提出并讨论了Ｌ_２（０，Ｔ）子空间上的三个最小范数问题，得到了这些问题的解，并给出了定理３在分布参数最优控制问题上的应用。     

同步发电机机械参数辨识初探——可辨识性分析

选取特定的数学模型 ,进行同步发电机机械参数可辨识性分析 ,得出该模型下可唯一辨识的结论 ,为同步发电机机械参数的辨识奠定了理论基础 ,同时也验证了该数学模型选择的可用性。     

A Bayesian Approach for Multiple Response Surface Optimization in the Presence of Noise Variables

An approach for the multiple response robust parameter design problem based on a methodology by Peterson (2000) is presented. The approach is Bayesian, and consists of maximizing the posterior predictive probability that the process satisfies a set of constraints on the responses. In order to find a solution robust to variation in the noise variables, the predictive density is integrated not only with respect to the response variables but also with respect to the assumed distribution of the noise variables. The maximization problem involves repeated Monte Carlo integrations, and two different methods to solve it are evaluated. A Matlab code was written that rapidly finds an optimal (robust) solution in case it exists. Two examples taken from the literature are used to illustrate the proposed method.     

确定线性多变量系统结构参数的递推辅助变量算法

本文研究了多变量系统中确定结构参数的递推辅助变量方法。文中采用的模型是输入输出差分方程的一种规范形式。根据Ahmed的结构辨识算法,文中给出了一个改进的算法,此算法是递推形式的,因而大大减少了计算量。