Robust Second Order Rotatable Designs : Part I

Abstract

In Panda and Das (Cal. Statist. Assoc. Bull., 44, 1994, 83-101) a study of rotatable designs with correlated errors was initiated and a systematic study of first order rotatable designs was attempted. Various correlated structures of the errors were considered.

This two-part article relates to a thorough study on robust second order rotatable designs (SORD's) under violation of the usual homoscedasticity assumption of the distribution of errors. Under a suitable autocorrelated structure of the dispersion matrix of the error components, we examine existence and construction of robust rotatable designs.

In part I, general conditions for rotatability have been derived and special cases have been examined under autocorrelated structure of the errors. Starting with the usual SORD's (under the uncorrelated error setup), we have discussed a method of construction of SORD's with correlated errors under the autocorrelated structure. An illustrative example is given at the end.

In part II,we propose to examine robustness of the usual SORD's with emphasis on properties such as weak rotatability, with due consideration as to the cost involved.