Efficient and optimal designs for correlated observations.

This thesis considers some aspects of the problem of finding efficient and optimal designs when observations are correlated. The two main areas that are examined are nested row-column (NRC) designs and early generation variety trials (EGVTs). In NRC designs, the experimental area is divided into b blocks, and each block is divided into P1 rows and P2 columns (blocks of size P1 x P2). Here, optimal NRC designs, which can be constructed from semi-balanced arrays, are obtained under the assumption that within-block observations are correlated. For a stationary reflection symmetric dependence structure, optimal NRC designs with blocks of size 2 x 2 are obtained for models with fixed block effects, which may also include row and/or column effects. It is shown that the efficiency of binary designs can be very low for some correlation values. Also, optimal NRC designs for blocks of size 3 x 3 and P1 x 2 (P1 ≥ 3 ) are determined. The optimality region for blocks of size P1 x P2 (P1 P2 ≥ 2) under the AR( 1)* AR( 1) process is also specified. It is shown that optimal NRC designs are highly specific to the correlation values. The purpose of EGVTs is to select top performing new crop varieties for further testing. Recently there has been much interest in the spatial analysis of EGVTs, but there has been little work on the design of efficient EGVTs when a spatial analysis is intended. Several intuitively simple criteria to assess the efficiency of designs for EGVTs are examined, and simulation studies suggest that some of these criteria are well associated with probabilities of selecting the highest yielding new varieties. Also, the efficiency and robustness of some systematic designs for EGVTs is investigated over several models and dependence structures. For the examples considered, it is shown that designs in which the plots containing control varieties are at least a knight's move apart are robust.