On E(s)-optimal supersaturated designs

A popular measure to assess 2-level supersaturated designs is the E(s²)$E(s^2)$ criterion. In this paper, improved lower bounds on E(s²)$E(s^2)$ are obtained. The same improvement has recently been established by Ryan and Bulutoglu [2007. E(s²)$E(s^2)$-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference 137, 2250–2262]. However, our analysis provides more details on precisely when an improvement is possible, which is lacking in Ryan and Bulutoglu [2007. E(s²)$E(s^2)$-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference 137, 2250–2262]. The equivalence of the bounds obtained by Butler et al. [2001. A general method of constructing E(s²)$E(s^2)$-optimal supersaturated designs. J. Roy. Statist. Soc. B 63, 621–632] (in the cases where their result applies) and those obtained by Bulutoglu and Cheng [2004. Construction of E(s²)$E(s^2)$-optimal supersaturated designs. Ann. Statist. 32, 1662–1678] is established. We also give two simple methods of constructing E(s²)$E(s^2)$-optimal designs.     

Resolution v.2 search designs

A fractional factorial design is called a resolution V.2 plan if it is capable of estimating all main effects and two-factor interaction effects, plus two three-factor interaction effects, In this paper, a necessary and sufficient condition for such a resolution V.2 plan is given, Furthermore, a new class of two-level resolution V.2 designs is proposed, We prove that the proposed design always satisfies such a necessary and sufficient condition, A comparison of run size between designs of resolutions VII and V.2 is made, It is shown that run size for design of resolution V.2 is significantly smaller.     

Lower Bounds on the Symmetric L 2-Discrepancy and Their Application

The role of uniformity measured by the symmetric L ₂-discrepancy given in Hickernell (1998 Hickernell , F. J. (1998). A generalized discrepancy and quadrature error bound. Math. Computat. 67:299–322.[Crossref], [Web of Science ®] , [Google Scholar]) has been studied in fractional factorial designs. The issue of lower bounds on the symmetric L ₂-discrepancy is crucial in the construction of uniform designs. This article reports some new lower bounds on the symmetric L ₂-discrepancy for symmetric fractional factorials and for a set of asymmetric fractional factorials. It is valuable to use these lower bounds to measure uniformity of given designs.     

Combination of multiple scores for nonparametric testing in multivariate linear regression set-up

For the problem of testing absence of x.egression under the p-variate nonparametric linear regression set-up involving m predictors, standard rank test criteria are in the form of a quadratic form in mp linear rank statistics. Different standard tests correspond to different choices of one system of scores for each variable. In this paper we propose two test criteria which are based on simultaneous choice of more than one system of scores for each variable. The criteria are obtained by applying the union-intersection technique in two different ways. It turns out that for either criterion the use of several systems of scores for each variable results in an improvement in the asymptotic power.     

Perception,Preference, and Patriotism: An Exploratory Analysis of the 1980 Winter Olympics

This article analyzes scores given by judges of figure skating at the 1980 Winter Olympics. Judges' scores are found to be highly correlated, with little evidence of scoring along political lines. However, an analysis of variance shows a small but consistent “patriotic” bias; judges tend to give higher scores to contestants from their own country. The influence of such effects on final placings is estimated.     

Note on Second-Order Polynomial Regression Models

Polynomial regression models have applications in the social sciences and in business research. Unfortunately, such models have a high degree of multicollinearity that creates problems with the statistical assessment of the model. In fact, the collinearity may be so severe that it could lead to an incorrect conclusion that some of the terms in the model are not statistically significant and should therefore be omitted from the model. This note provides a simple transformation to achieve orthogonality in polynomial models between the linear and quadratic terms, thereby eliminating the collinearity problem. It also shows that the same procedure does not achieve orthogonality for higher-order terms. An example data set is analyzed to show the benefits of such a procedure.