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October 1997 Optimal exact designs on a circle or a circular arc
Huaiqing Wu
Ann. Statist. 25(5): 2027-2043 (October 1997). DOI: 10.1214/aos/1069362385


Fitting a circle to a set of data points on a plane is very common in engineering and science. An important practical problem is how to choose the locations of measurement on a circular feature. So far little attention has been paid to this design issue and only some simulation results are available. In this paper, for Berman's bivariate four-parameter model, $\Phi$-optimality is defined and shown to be equivalent to all $\phi_p$-criteria with $p \epsilon [-\infty, 1)$. Then $\Phi$-optimal exact designs on a circle or a circular arc are derived for any sample size and sampling range. As a by-product, $\Phi$-optimal approximate designs are also obtained. These optimal designs are used to evaluate the efficiency of the equidistant sampling method widely used in practice. These results also provide guidelines for users on sampling method and sample size selection.


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Huaiqing Wu. "Optimal exact designs on a circle or a circular arc." Ann. Statist. 25 (5) 2027 - 2043, October 1997.


Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0882.62072
MathSciNet: MR1474081
Digital Object Identifier: 10.1214/aos/1069362385

Primary: 62K05

Keywords: $\phi$-optimality , $\phi_p$-criteria , efficiency , equidistant sampling , optimal design , orthogonal design

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 5 • October 1997
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