The Annals of Statistics
- Ann. Statist.
- Volume 29, Number 2 (2001), 577-594.
Optimality of partial geometric designs
We find a sufficient condition on the spectrum of a partial geometric design d* such that, when d* satisfies this condition, it is better (with respect to all convex decreasing optimality criteria) than all unequally replicated designs (binary or not) with the same parameters b, v, k as d*.
Combining this with existing results, we obtain the following results:
(i) For any q \ge 3, a linked block design with parameters b = q2, v = q2 + q, k = q2 -1 is optimal with respect to all convex decreasing optimality criteria in the unrestricted class of all connected designs with the same parameters.
(ii) A large class of strongly regular graph designs are optimal w.r.t. all type 1 optimality criteria in the class of all binary designs (with the given parameters). For instance, all connected singular group divisible (GD) designs with \lambda_1 = \lambda_2 + 1 (with one possible exception) and many semiregular GD designs satisfy this optimality property.
Specializing these general ideas to the Acriterion, we find a large class of linked block designs which are Aoptimal in the unrestricted class. We find an even larger class of regular partial geometric designs (including, for instance, the complements of a large number of partial geometries) which are Aoptimal among all binary designs.
Ann. Statist. Volume 29, Number 2 (2001), 577-594.
First available in Project Euclid: 24 December 2001
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62K05: Optimal designs
Secondary: 15A42: Inequalities involving eigenvalues and eigenvectors
Bagchi, Bhaskar; Bagchi, Sunanda. Optimality of partial geometric designs. Ann. Statist. 29 (2001), no. 2, 577--594. doi:10.1214/aos/1009210554. http://projecteuclid.org/euclid.aos/1009210554.