Estimating treatment effects on optimal row designs under dependence

Abstract

The experimental units or simply units are arranged in time or along a line with every unit to be allocated one out of v treatments. The aim is to find the design which gives optimal estimates of treatments effects or of treatment differences. The main effects model with homogeneous population, when the observations follow a first-order autoregressive process, with positive or negative parameter p, is used. Universal optimality and other optimality are defined and shown that for positive p, the Williams IIa designs, which are A- and D-optimal for estimating treatment contrasts, are not A- or E-optimal for estimating treatment effects. In order to estimate treatment effects a shortened Williams design is applied by considering the first or last unit as the right alternative. In the case of three treatments and negative dependence, optimal designs are presented for any number of units.