A general method of constructing E(s2)-optimal supersaturated designs

There has been much recent interest in supersaturated designs and their application in factor screening experiments. Supersaturated designs have mainly been constructed by using the E ( s ²)-optimality criterion originally proposed by Booth and Cox in 1962. However, until now E ( s ²)-optimal designs have only been established with certainty for n experimental runs when the number of factors m is a multiple of n-1 , and in adjacent cases where m = q ( n -1) + r (| r | 2, q an integer). A method of constructing E ( s ²)-optimal designs is presented which allows a reasonably complete solution to be found for various numbers of runs n including n ,=8 12, 16, 20, 24, 32, 40, 48, 64.     

A simple way to obtain the spectral decomposition of variance components models for balanced data

By means of an example it is shown how eigenvalues and eigenvectors of variance components models can be obtained straightforwardly when balanced data are available. Simple asymptotically efficient estimators of the variance components are presented.     

Asymptotic tests and monte carlo studies associated with the multiplicative interaction model

Several authors have proposed approximations to percentage points required for testing certain hypotheses associated with the multiplicative interaction model. Alternative approximations based on the asymptotic joint distribution of the characteristic roots of a noncentral Wishart matrix are proposed in this paper. The type I error rates of the resulting tests and the existing procedures are then compared using Monte Carlo methods.     

非负矩阵谱半径的新估计

对于非负矩阵的谱半径进行研究,分析了文[1,2]中的结果,给出了非负矩阵谱半径的新估计,该结果改进了文[1,2]中的相关结果.     

G（3）的存在性定理及其结构规律

给出了３度平面图的两个存在性定理的简洁证明，以矩阵列举法迅速得到所有的异构类，并举例说明结论的意义．     

Detection and Interpretation of a Multivariate Signal Using Combined Charts

A control procedure is presented in this article that is based on jointly using two separate control statistics in the detection and interpretation of signals in a multivariate normal process. The procedure detects the following three situations: (i) a mean vector shift without a shift in the covariance matrix; (ii) a shift in process variation (covariance matrix) without a mean vector shift; and (iii) both a simultaneous shift in the mean vector and covariance matrix as the result of a change in the parameters of some key process variables. It is shown that, following the occurrence of a signal on either of the separate control charts, the values from both of the corresponding signaling statistics can be decomposed into interpretable elements. Viewing the two decompositions together helps one to specifically identify the individual components and associated variables that are being affected. These components may include individual means or variances of the process variables as well as the correlations between or among variables. An industrial data set is used to illustrate the procedure.     

On estimating the covariance matrix of robust regression M-estimates

By analyzing a special class of regression problems we point out that previously suggested estimates of the covariance matrix of regression M-cstimatos are inadequate for certain design matrices. These results confirm the conclusions drawn in several Monte Cailo studies.     

Unbiased F Tests for Factorial Experiments for Correlated Data

This paper finds a general form of the correlation matrix that may be used to provide unbiased F tests in a.k-way factorial experiment.