The Annals of Statistics

Universal optimality of Patterson’s crossover designs

Kirti R. Shah, Mausumi Bose, and Damaraju Raghavarao

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Abstract

We show that the balanced crossover designs given by Patterson [Biometrika 39 (1952) 32–48] are (a) universally optimal (UO) for the joint estimation of direct and residual effects when the competing class is the class of connected binary designs and (b) UO for the estimation of direct (residual) effects when the competing class of designs is the class of connected designs (which includes the connected binary designs) in which no treatment is given to the same subject in consecutive periods. In both results, the formulation of UO is as given by Shah and Sinha [Unpublished manuscript (2002)].

Further, we introduce a functional of practical interest, involving both direct and residual effects, and establish (c) optimality of Patterson’s designs with respect to this functional when the class of competing designs is as in (b) above.

Article information

Source
Ann. Statist., Volume 33, Number 6 (2005), 2854-2872.

Dates
First available in Project Euclid: 17 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1140191676

Digital Object Identifier
doi:10.1214/009053605000000723

Mathematical Reviews number (MathSciNet)
MR2253105

Zentralblatt MATH identifier
1084.62066

Subjects
Primary: 62K05: Optimal designs
Secondary: 62K10: Block designs

Keywords
Direct treatment effects residual treatment effects repeated measurement designs optimal joint estimation of effects

Citation

Shah, Kirti R.; Bose, Mausumi; Raghavarao, Damaraju. Universal optimality of Patterson’s crossover designs. Ann. Statist. 33 (2005), no. 6, 2854--2872. doi:10.1214/009053605000000723. https://projecteuclid.org/euclid.aos/1140191676


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