Robust second-order slope-rotatable designs with maximum directional variance
Abstract
In response surface methodology, rotatability and slope-rotatability are natural and highly desirable properties for second-order regression models. In this article, we introduce the concept of robust slope-rotatable designs with equal maximum directional variance for second-order response surface models with correlated observations. This requires that the maximum variance of the estimated slope over all possible directions to be only a function of the distance of the point from the design origin, and independent of correlation parameter or parameters involved in the variance-covariance matrix of errors. It is derived that robust second-order rotatable designs of two factors are also robust slope-rotatable designs with equal maximum directional variance. It is also established that within the robust second-order symmetric balanced designs, robust rotatable designs are also robust slope-rotatable with equal maximum directional variance for more than two factors. We also investigate a class of robust second-order slope-rotatable designs with equal maximum directional variance for special correlation structures of errors.
Publication Title
Communications in Statistics - Theory and Methods
Recommended Citation
Das, R., Park, S., & Aggarwal, M. (2010). Robust second-order slope-rotatable designs with maximum directional variance. Communications in Statistics - Theory and Methods, 39 (5), 803-814. https://doi.org/10.1080/03610920902796064
