The Annals of Mathematical Statistics

On the Nonrandomized Optimality and Randomized Nonoptimality of Symmetrical Designs

J. Kiefer

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Abstract

Many commonly employed symmetrical designs such as Balanced Incomplete Block Designs (BIBD's), Latin Squares (LS's), Youden Squares (YS's), etc., are shown to have optimum properties among the class of non-randomized designs (Section 3). This represents an extension of a property first proved by Wald for LS's in [1]; a similar property demonstrated by Ehrenfeld for LS's in [2] (as well as a third optimum property considered here) is shown to be an immediate consequence of the Wald property, and the Wald property is shown to be the more relevant when one considers optimality rigorously (Section 2). Surprisingly, all of these optimum properties fail to hold if randomized designs are considered (Section 4); the results of Sections 2 and 3, as well as those appearing previously in the literature (as in [1], [2], [3]) must be interpreted in this sense. Generalizations of the BIBD's and YS's, for which analogous results hold, are introduced.

Article information

Source
Ann. Math. Statist. Volume 29, Number 3 (1958), 675-699.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177706530

Digital Object Identifier
doi:10.1214/aoms/1177706530

Mathematical Reviews number (MathSciNet)
MR98451

Zentralblatt MATH identifier
0092.36102

JSTOR
links.jstor.org

Citation

Kiefer, J. On the Nonrandomized Optimality and Randomized Nonoptimality of Symmetrical Designs. Ann. Math. Statist. 29 (1958), no. 3, 675--699. doi:10.1214/aoms/1177706530. http://projecteuclid.org/euclid.aoms/1177706530.


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