A NEW MEASURE OF ROTATABILITY OF RESPONSE SURFACE DESIGNS

This paper proposes a new measure of rotatability of a response surface design. It is based on a comparison between the design moments of a given design and the design moments of a rotatable design closest to the given design in the least squares sense. This measure is easier to calculate than Khurľs measure. An alternative easier non-geometrical way of deriving Khuri's measure is also presented. Both measures are calculated to illustrate some designs considered by Khuri.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72828/1/j.1467-842X.1996.tb00366.x.pd

Foundations for the Theory of Least Squares

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147086/1/rssb00768.pd

Breit - Wigner parameters of nucleon resonance S11(1535)

The result of partial - wave analysis of angular distributions for the process gamma+p -> eta +p at the energies upto 2 GeV are given. From the energy dependence of the regression coefficient a0(W) the reliable estimates of Breit - Wigner parameters of S11(1535) - resonance and energy dependence of real and imagenery parts of electric dipol amplitude E0+ and its phase were obtainedComment: 12 pages, 11 figure

The analysis of very small samples of repeated measurements II: a modified box correction

There is a need for appropriate methods for the analysis of very small samples of continuous repeated measurements. A key feature of such analyses is the role played by the covariance matrix of the repeated observations. When subjects are few it can be difficult to assess the fit of parsimonious structures for this matrix, while the use of an unstructured form may lead to a serious lack of power. The Kenward-Roger adjustment is now widely adopted as a means of providing an appropriate inferences in small samples, but does not perform adequately in very small samples. Adjusted tests based on the empirical sandwich estimator can be constructed that have good nominal properties, but are seriously underpowered. Further, when such data are incomplete, or unbalanced, or non-saturated mean models are used, exact distributional results do not exist that justify analyses with any sample size. In this paper, a modification of Box's correction applied to a linear model based $F$-statistic is developed for such small sample settings and is shown to have both the required nominal properties and acceptable power across a range of settings for repeated measurements

Comparison of Tukey's T-Method and Scheffé's S-Method for Various Numbers of All Possible Differences of Averages Contrasts Under Violation of Assumptions

Empirical .05 and .01 rates of Type I error were compared for the Tukey and Scheffé multiple comparison techniques. The experimentwise error rate was defined over five sets of the all possible 25 differences of averages contrasts. The robustness of the Tukey and Scheffé statistics was not only related to the type of assumption violation, but also to the sets containing different numbers of contrasts. The Tukey method could be judged as robust a statistic as the Scheffé method.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Simultaneous confidence tubes in multivariate linear regression

Simultaneous confidence bands have been shown in the statistical literature as powerful inferential tools in univariate linear regression. While the methodology of simultaneous confidence bands for univariate linear regression has been extensively researched and well developed, no published work seems available for multivariate linear regression. This paper fills this gap by studying one particular simultaneous confidence band for multivariate linear regression. Because of the shape of the band, the word ‘tube’ is more pertinent and so will be used to replace the word ‘band’. It is shown that the construction of the tube is related to the distribution of the largest eigenvalue. A simulation-based method is proposed to compute the 1 − α quantile of this eigenvalue. With the computation power of modern computers, the simultaneous confidence tube can be computed fast and accurately. A real-data example is used to illustrate the method, and many potential research problems have been pointed out