A-optimal block designs for the comparison of treatments with a control with autocorrelated errors
Joachim Kunert (TU Dortmund)
Friday 21st October, 2011 15:00-16:00 Maths 203
There is an extensive literature on optimal and efficient designs for comparing /v/ test (or new) treatments with a control (or standard treatment) - see Majumdar (1996). However, almost all results assume the observations are uncorrelated. We consider block experiments with /b/ blocks of size /k/ and the situation that the observations in the same block are positively correlated under a first-order autoregressive process AR(1). We further assume generalised least-squares estimation for a known dependence. We determine approximate designs, assuming that the number of blocks /b/ is large enough for an optimal design to exist, and consider the form of that optimal design. This method may lead to exact optimal designs for some /b/, /v/, /k/, but usually will only indicate the structure of an efficient design for any particular /b/, /v/, /k/, and yield an efficiency bound, usually unattainable. The bound and the structure can then be used to investigate efficient finite designs.