With a personal account, you can read up to 100 articles each month for free.
Already have an account?
- Access everything in the JPASS collection
- Read the full-text of every article
- Download up to 10 article PDFs to save and keep
- Access everything in the JPASS collection
- Read the full-text of every article
- Download up to 120 article PDFs to save and keep
Purchase a PDF
How does it work?
- Select the purchase option.
-
Check out using a credit card or bank account with
PayPal . - Read your article online and download the PDF from your email or your account.
Connectedness is an important property which every block design must possess if it is to provide an unbiased estimator for all elementary treatment contrasts under the usual linear additive model. We have classified the family of connected designs into three subclasses: locally connected, globally connected and pseudo-globally connected designs. Basically, a locally connected design is one in which not all the observations participate in the estimation. A globally connected design is one in which all observations participate in the estimation. Finally, a pseudo-globally connected design is a compromise between locally and globally connected designs. Theorems and corollaries are given which characterize the different classes of connected designs. In our discussion on the optimality of connected designs we show that there is much to be gained by partitioning the family of connected designs in the above fashion. Our optimality criteria are S-optimality suggested by Shah, which selects the design with minimum trace of the information matrix squared and (M, S)-optimality which selects the S optimal design from the class of designs with maximum trace of the information matrix. Using these optimality criteria, we have been able to derive some new results which we hope to be of interest to the users and researchers in the field of optimum design theory. To be specific, let BD {v, b, (ri), (ku)} denote a block design on a set of v treatments with b blocks of size ku, u = 1,2, ⋯, b and treatment i is replicated ri times. Then we have shown that for the family of connected block designs BD {v, b, (ri), k} with (i) less than k - 1 treatments having replication equal to one and binary (0, 1) the S-optimum design is pseudo-globally connected; (ii) the S-optimum design is globally connected if $r_i > 1$ and the designs are binary; and (iii) at least one treatment with replication greater than b, then the (M, S)-optimum design is pseudo-globally connected. In the final part of this paper we mention some unsolved problems in this area.
The Annals of Statistics publishes research papers of the highest quality reflecting the many facets of contemporary statistics. Primary emphasis is placed on importance and originality, not on formalism. The discipline of statistics has deep roots in both mathematics and in substantive scientific fields. Mathematics provides the language in which models and the properties of statistical methods are formulated. It is essential for rigor, coherence, clarity and understanding. Consequently, our policy is to continue to play a special role in presenting research at the forefront of mathematical statistics, especially theoretical advances that are likely to have a significant impact on statistical methodology or understanding. Substantive fields are essential for continued vitality of statistics since they provide the motivation and direction for most of the future developments in statistics. We thus intend to also publish papers relating to the role of statistics in interdisciplinary investigations in all fields of natural, technical and social science. A third force that is reshaping statistics is the computational revolution, and The Annals will also welcome developments in this area.
The purpose of the Institute of Mathematical Statistics (IMS) is to foster the development and dissemination of the theory and applications of statistics and probability. The Institute was formed at a meeting of interested persons on September 12, 1935, in Ann Arbor, Michigan, as a consequence of the feeling that the theory of statistics would be advanced by the formation of an organization of those persons especially interested in the mathematical aspects of the subject. The Annals of Statistics and The Annals of Probability (which supersede The Annals of Mathematical Statistics), Statistical Science, and The Annals of Applied Probability are the scientific journals of the Institute. These and The IMS Bulletin comprise the official journals of the Institute. The Institute has individual membership and organizational membership. Dues are paid annually and include a subscription to the newsletter of the organization, The IMS Bulletin. Members also receive priority pricing on all other IMS publications.
This item is part of a JSTOR Collection.
For terms and use, please refer to our
The Annals of Statistics
© 1974 Institute of Mathematical Statistics