On Φ_p-optimality of Incomplete Block Designs: An Algorithm

Abstract

Since statisticians are interested in optimal incomplete block designs, the existence of algorithms to construct them can be notable. This article presents an algorithm to search for Φ_p-optimal or nearly Φ_p-optimal incomplete block designs. It is a variant of exchange and interchange procedures of Jones and Eccleston. The algorithm starts by constructing a cyclic design as the initial design. Then it enters a modified exchange and interchange procedures. Since our criterion for optimality is Φ_p, the algorithm utilizes the eigenvalues of the information matrix of designs. In most of the cases, optimal or nearly optimal designs were found, which shows the good performance of the algorithm. In addition, a new virtual design for has been obtained. So, for situations in which optimal incomplete block designs are required, this algorithm can be used.

Keywords:

• Exchange and interchange procedures
• Incomplete block design
• Information matrix
• Optimal designs
• Φ p-optimality.

Mathematics Subject Classification:

• 62Kxx; 62K05; 05B05