Construction of Optimal Balanced Incomplete Block Designs for Correlated Observations

Optimal Cylindrical-block Designs for Correlated Observations

This paper addresses the problem of characterizations and constructions of optimal and efficient two-dimensional designs for generalized least squares estimation of treatment contrasts when the errors are correlated. Universally optimal designs are obtained when the plots of each block are on a cylinder and the errors follow the three parameter autonormal process on the cylinder. Efficiencies o...

Construction of Balanced Incomplete Block Designs Using Cyclic Shifts

The construction of balanced incomplete block designs is considered using the method of cyclic shifts. An interesting feature of this method is that there is no need to construct the bocks of the actual design to obtain the properties of a design. One can obtain the off-diagonal elements of the concurrence matrix from the sets of shifts with less effort. A catalogue of balanced incomplete block...

Splitting balanced incomplete block designs

Optimal Incomplete Block Designs

Optimal incomplete block designs are pursued through the E-criterion of minimizing maximal variance. Methodology is developed for design choice based on graphs and an extensive catalog of downloadable designs compiled. Along with the general methodology, a near complete solution for E-optimal block designs is provided for up to 15 treatments. E-optimality is revealed as a flexible criterion tha...

Remarks on Balanced Incomplete Block Designs

Proof. Assume the hypothesis and the falsity of either conclusion. Construct matrix A of 2x + 2 rows and 4x+4 columns, with entries + 1 and — 1. The first column contains exclusively +1, and the second column — 1. Set up one-to-one correspondences between rows of A and elements of D ; between columns other than the first two of A and blocks of D. Enter +1 if the element is contained in the bloc...