On efficient robust first order rotatable designs with autocorrelated error

Generally, it is very difficult to derive optimal or at least efficient designs for linear models with correlated observations, and for some correlation structure, an exact DD-optimal design does not exist. In this paper we have developed the notion of a DD-optimal robust first order design   (DD-ORFOD) for linear model with a general correlated error structure. We have shown that DD-optimal robust first order designs are always robust first order rotatable designs (RFORDs) but the converse is not always true. For a first order linear model with autocorrelated error, we have developed a set of efficient   RFORDs with efficiency around ninety percent and the developed designs are very close to DD-ORFODs. We have also developed a new method of analysis that is the estimation of regression parameters, correlation parameter and error variance, assuming the correlation parameter involved in the correlation structure is unknown.