Some sufficient conditions for the type 1 optimality of block designs |
| |
Authors: | Mike Jacroux |
| |
Institution: | Washington State University, Pullman, WA 99164-2930, USA |
| |
Abstract: | In this paper, we investigate the problem of determining block designs which are optimal under type 1 optimality criteria within various classes of designs having υ treatments arranged in b blocks of size k. The solutions to two optimization problems are given which are related to a general result obtained by Cheng (1978) and which are useful in this investigation. As one application of the solutions obtained, the definition of a regular graph design given in Mitchell and John (1977) is extended to that of a semi-regular graph design and some sufficient conditions are derived for the existence of a semi-regular graph design which is optimal under a given type 1 criterion. A result is also given which shows how the sufficient conditions derived can be used to establish the optimality under a specific type 1 criterion of some particular types of semi- regular graph designs having both equal and unequal numbers of replicates. Finally,some sufficient conditions are obtained for the dual of an A- or D-optimal design to be A- or D-optimal within an appropriate class of dual designs. |
| |
Keywords: | Primary 62K05 Secondary 62K10 Type 1 optimality A-optimality D-optimality Block design Regular graph design Semi-regular graph design Dual |
本文献已被 ScienceDirect 等数据库收录! |
|