EWMA Chart and Measurement Error

Measurement error is a usually met distortion factor in real-world applications that influences the outcome of a process. In this paper, we examine the effect of measurement error on the ability of the EWMA control chart to detect out-of-control situations. The model used is the one involving linear covariates. We investigate the ability of the EWMA chart in the case of a shift in mean. The effect of taking multiple measurements on each sampled unit and the case of linearly increasing variance are also examined. We prove that, in the case of measurement error, the performance of the chart regarding the mean is significantly affected.     

椭圆曲线密码运算效率提高的算法实现

本文针对椭圆曲线密码系统的算法高速实现,讨论了对椭圆曲线上的点的加法和倍点运算,以及对点的标量乘法运算进行优化的技术,可以大大提高整个椭圆曲线密码系统的算法实现性能。     

D-optimal weighted paired comparison designs

As a generalization of the paired comparison designs, the experimental design which considers the weighted difference between responses is studied. D-optimal designs are constructed for a model with main effects and first-order interactions. The experimental region is a hypercube or a hypersphere.     

与点变换相切及密切的一维射影变换

射影变换在高等几何中是十分重要的。本文主要讨论三个问题:存在着无穷多个一维射影变换在一对对应的正则点对与一个已知点变换相切;存在着唯一个射影变换在一对对应的正则点对密切于一个已知的变换;与已知点变换逼近到三阶邻域或高于三阶邻域的一维射影变换必须满足一些条件。对于逼近过程的误差也给以考虑。     

海西区城市构建两岸区域金融中心竞争力比较

基于两岸关系、海西战略和有限资源约束,正确选择金融中心建设的备选城市是首要的,必须对各城市经济金融竞争力进行分析。通过选取31、27、11个指标,利用因子分析法和“断裂点”理论对海西区20个城市构建两岸金融中心竞争力、一般性区域金融中心竞争力、金融业发展竞争力三个层面进行分析,最后提出厦门构建两岸金融中心、福州构建海西区域金融中心、温州构建区域专业金融中心以及泉州和汕头发展为次级金融极等建议。     

Weighted L1-estimates for the First-order Bifurcating Autoregressive Model

We developed robust estimators that minimize a weighted L₁ norm for the first-order bifurcating autoregressive model. When all of the weights are fixed, our estimate is an L₁ estimate that is robust against outlying points in the response space and more efficient than the least squares estimate for heavy-tailed error distributions. When the weights are random and depend on the points in the factor space, the weighted L₁ estimate is robust against outlying points in the factor space. Simulated and artificial examples are presented. The behavior of the proposed estimate is modeled through a Monte Carlo study.     

Expected Absolute Error of the Usual Estimator of the Binomial Parameter

For X with binomial (n, p) distribution the usual measure of the error of X/n as an estimator of p is its standard error S_n(p) = √{E(X/n – p)²} = √{p(1 – p)/n}. A somewhat more natural measure is the average absolute error D_n(p) = E‖X/n – p‖. This article considers use of D_n(p) instead of S_n(p) in a student's first introduction to statistical estimation. Exact and asymptotic values of D_n(p), and the appearance of its graph, are described in detail. The same is done for the Poisson distribution.     

The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator

It is well known that the ordinary least squares estimator of Xβ in the general linear model E _y = Xβ, cov y = σ² V, can be the best linear unbiased estimator even if V is not a multiple of the identity matrix. This article presents, in a historical perspective, the development of the several conditions for the ordinary least squares estimator to be best linear unbiased. Various characterizations of these conditions, using generalized inverses and orthogonal projectors, along with several examples, are also given. In addition, a complete set of references is provided.     

一种加权主成分距离的聚类分析方法

指标之间的高度相关性及其重要性差异导致了传统聚类分析方法往往无法获得良好的分类效果。本文在对传统聚类分析方法及其各种改进方法局限性展开探讨的基础上,运用数学方法重构了分类定义中的距离概念,通过定义自适应赋权的主成分距离为分类统计量,提出一种新的改进的主成分聚类分析方法——加权主成分距离聚类分析法。理论研究表明,加权主成分距离聚类分析法系统集成了已有聚类分析方法的优点,有充分的理论基础保证其科学合理性。仿真实验结果显示,加权主成分距离聚类分析法能够有效解决已有聚类分析方法在特定情形下的失真问题,所得分类效果更为理想。     

On Complete Convergence for Weighted Sums of NA Random Fields

In this paper, we prove the complete convergence for the weighted sums of negatively associated random variables with multidimensional indices. The main result generalizes Theorem 2.1 in Kuczmaszewska and Lagodowski (2011 Kuczmaszewska, A., Lagodowski, Z.A. (2011). Convergence rates in the SLLN for some classes of dependent random field. J. Math. Anal. Appl. 380:571–584.[Crossref], [Web of Science ®] , [Google Scholar]) to the case of weighted sums.