The Annals of Statistics

Minimaxity for Randomized Designs: Some General Results

Ker-Chau Li

Full-text: Open access

Abstract

In many design settings where model violations are present, a "stochastic" minimaxity for many standard randomization procedures is demonstrated. This result requires no special analytic properties of the loss function and estimators. Next, under the squared loss and with the restriction to the use of linear estimators, a recipe for finding a randomized strategy is given. As a special case, randomizing an $A$-optimal design in the standard manner and using the least squares estimates yields a minimax strategy in most cases. These results generalize some aspects of Wu (1981).

Article information

Source
Ann. Statist., Volume 11, Number 1 (1983), 225-239.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346073

Digital Object Identifier
doi:10.1214/aos/1176346073

Mathematical Reviews number (MathSciNet)
MR684880

Zentralblatt MATH identifier
0517.62077

JSTOR
links.jstor.org

Subjects
Primary: 62K99: None of the above, but in this section
Secondary: 62A05 62C20: Minimax procedures

Keywords
$A$-optimality doubly transitive groups $H$-uniform randomization randomization procedures randomized strategies robustness

Citation

Li, Ker-Chau. Minimaxity for Randomized Designs: Some General Results. Ann. Statist. 11 (1983), no. 1, 225--239. doi:10.1214/aos/1176346073. https://projecteuclid.org/euclid.aos/1176346073


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