Standard errors for EM estimation

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM in algorithm seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.     

On the analysis of multivariate repeated measures designs

The relationship between the mixed-model analysis and multivariate approach to a repeated measures design with multiple responses is presented. It is shown that by taking the trace of the appropriate submatrix of the hypothesis (error) sums of squares and crossproducts (SSCP) matrix obtained from the multivariate approach, one can get the hypothesis (error) SSCP matrix for the mixed-model analysis. Thus, when analyzing data from a multivariate repeated measures design, it is advantageous to use the multivariate approach because the result of the mixed-model analysis can also be obtained without additional computation.     

Phase-shifting common cycles and common trends

In this paper, we outline a framework for modelling and analysing economic fluctuations and dynamics. It is assumed that there may exist common trends and common cycles in the time series to be analysed It is further generalised that common cycles may have non-coincident, or phase-shifting attributes These attributes are examined via the Markov transition matrix in a VAR system, revealing the way in which the phase-shifting works with the reduced rank Markov transition matrix. The links with the structural common trend model are also presented.     

基于Shapley值法的移动增值服务价值链利润分配模型

研究对象为任意节点连接和任意支撑的平面框架。一般梁单元由等截面直杆及其杆端的轴向弹簧、切向弹簧和转动弹簧组成，推导得到此类单元的刚度矩阵、单元在8种基本荷载作用下的等效节点荷载。采用Matlab语言编写了适用于一般节点非线性连接框架的静力分析程序，非线性形式为指数函数或多项式函数，可以得到结构不同连接刚度下的节点位移、杆端位移和杆端力。算例显示出节点柔度对结构受力和变形的影响。     

Marginally oversaturated designs

A special class of supersaturated design, called marginally over saturated design (MOSD), in which the number of variables under investigation (k) is only slightly larger than the number of experimental runs (n), is presented. Several optimality criteria for supersaturated designs are discussed. It is shown that the resolution rank criterion is most appropriate for screening situations. The construction method builds on two major theorems which provide an efficient way to evaluate resolution rank. Examples are given for the cases n=8, 12, 16, and 20. Potential extensions for future work are discussed.     

基于线性矩阵不等式的牵制控制策略分析

研究复杂动力学网络的同步牵制控制问题.通过引入牵制控制,对具有大规模节点网络中的小部分节点实施线性反馈控制策略,使得整个网络的所有节点均达到同步.针对一类一致连结的耦合复杂网络模型,采用线性矩阵不等式的方法给出了实施牵制控制达到同步的充分条件.该条件表明,选择牵制异质网络中度较大的节点可能更容易使得网络实现同步.特别地,对于特定的内部耦合矩阵和足够大的耦合强度,只要对网络中任一节点实施牵制控制就可以保证整个网络同步的实现.数值仿真验证了上述结论的有效性.     

A study of BIB designs through support matrices

This paper deals with the existence and nonexistence of BIB designs with repeated blocks. The approach is an algebraic one. The concept of a support matrix is introduced and some of its basic properties are noted. Some basic examples of support matrices are given when the block size is 3. The connection between full column rank proper support matrices and irreducible designs is explored and some examples of such matrices are given.     

AN ALGORITHMIC APPROACH TO BAYESIAN LINEAR MODEL CALCULATIONS

A framework is described for organizing and understanding the computations necessary to obtain the posterior mean of a vector of linear effects in a normal linear model, conditional on the parameters that determine covariance structure. The approach has two major uses; firstly, as a pedagogical tool in the derivation of formulae, and secondly, as a practical tool for developing computational strategies without needing complicated matrix formulae that are often unwieldy in complex hierarchical models. The proposed technique is based upon symbolic application of the sweep operator SWP to an appropriate tableau of means and covariances. The method is illustrated with standard linear model specifications, including the so-called mixed model, with both fixed and random effects.     

二次型与(半)稳定矩阵的判定

对二次型与（半）稳定矩阵之间的相互关系进行了讨论，得到了二者之间的相互判定方法，且利用二次型的不同配方法得到判定（半）稳定矩阵的一些条件     

开放微带不连续电路的三端口网络描述

给出了开放微带不连续电路的三端口网络描述。将微带电路向空间的辐射作为一个端口来处理，成功地消除了由于忽略电路的空间辐射效应引入的电路数字模拟误差。利用时域有限差分法（ＦＤＴＤ）一次运算就可得出三端口网络的Ｓ参数矩阵的各元素，而无需任何预处理，大大地节省了ＣＰＵ时间。实际计算与已发表的数据吻合得很好，表明文中给出的三端口定义是合理有效的。此三端口微带电路的定义可容易地推广到其他非屏蔽传输线电路的分析，可广泛用于电磁兼容分析、微带天线及其他开放传输线电路的ＣＡＤ技术中。