On optimality and construction of row designs under dependence for estimating means.

In row designs, n experimental units are arranged in time or along a line. Every experimental unit is allocated to one out of ν treatments. The purpose of this paper is to determine optimal row designs for estimating means, that is treatment effects, under the model of main effects with homogeneous population. The errors of the observations follow a first-order autoregressive process with parameter ρ. For ν = 3 , we show that the design d (3 m) : 1 3 2 ⋯ 1 3 2 ⏟ 3 m is D-optimal, when n = 3m, for any 0 < ρ < 1 and any m ≥ 2. Also, we find and construct the A-optimal designs, when n = 3m, for any 0 < ρ < 1 and any m ≥ 2. Moreover, we prove that the designs d (3 m + 1) : 1 3 2 ⋯ 1 3 2 ⏟ 3 m 1 and d (3 m + 2) : 1 2 3 ⋯ 1 2 3 ⏟ 3 m 12 are D-optimal, when n = 3m + 1 and n = 3m + 2, respectively, for any 0 < ρ < 1 and any m ≥ 1. Furthermore, we present the competing designs for some values of n, when ν ≥ 4 and − 1 < ρ < 1. [ABSTRACT FROM AUTHOR]