Spacing of Information in Polynomial Regression

Garza, A. de la

doi:10.1214/aoms/1177728851

Cited by 74 publications

(25 citation statements)

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“…This result corresponds to the contribution of De la Garza (1954) and Silvey (1980) in the conventional optimal design framework for finding the number and weight of support points of a D-optimal design. The proof of Theorem 1 can be found in Appendix A.1.…”

Section: Optimal Design For Mar Mechanisms With Complete Case Analysismentioning

confidence: 53%

Optimal design for experiments with possibly incomplete observations

Lee¹,

Biedermann²,

Mitra³

2018

STAT SINICA

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Missing responses occur in many industrial or medical experiments, for example in clinical trials where slow acting treatments are assessed. Finding efficient designs for such experiments is problematic since it is not known at the design stage which observations will be missing. The design literature mainly focuses on assessing robustness of designs for missing data scenarios, rather than finding designs which are optimal in this situation. Imhof, Song and Wong (2002) propose a framework for design search, based on the expected information matrix. We develop a new approach which includes Imhof, Song and Wong (2002)'s method as special case and justifies its use retrospectively. Our method is illustrated through a simulation study based on real data from an Alzheimer's disease trial.

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Section: Optimal Design For Mar Mechanisms With Complete Case Analysismentioning

confidence: 53%

Optimal design for experiments with possibly incomplete observations

Lee¹,

Biedermann²,

Mitra³

2018

STAT SINICA

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“…It was showed by Garza (1954) that for the polynomial regression model of degree p with uncorrelated errors the dispersion matrix of the estimated polynomial coefficients can be attained by the spacing the information at only p + 1 values. The de la Garza phenomenon was used in the theory of optimal designs, for example in papers written by Luoma et al (2001), Mandal (2002).…”

Section: Extended Growth Curve Modelmentioning

confidence: 99%

Simultaneous choice of time points and the block design in the growth curve model

Szczepańska

2012

Stat Papers

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“…This result tells us that we need only to consider designs with finite support. For the polynomial regression problems, the design 'H needs only k+1 support points (de la Garza, 1954;Guest, 1958;Karlin and Studden, 1966b;Escobar and Cornette, 1983). …”

Section: Universi^mentioning

confidence: 99%

“…Optimal designs related to polynomials have also been studied extensively (e.g., de la Garza, 1954;Guest, 1958;Kiefer and Wolfowitz, 1959;Studden, 1966a, 1966b;Atwoad, 1969;Stigler, 1971;Kiefer and Studden, 1976;Studden, 1978Studden, , 1980Studden, , 1982. A very important characteristic of optimal design problems for polynomial regression is that the elements of M(%) are moments of the design measure.…”

Section: Ordinary Optimality Criteriamentioning

confidence: 99%

“…de la Garza (1954) showed that the G-optimal design for polynomial regressions of degree m with x = [-1,1] is given by the design which puts equal mass on + 1 and the (m-1) zeros of the first derivative of the Legendre polynomial of degree m. Guest (1958) obtained the D-optimal design for polynomial regression, which is exactly the same as the Goptimal design. Kiefer and Wolfowitz (1960) gave a proof of the equiva lence relation between D-optlmality and G-optlmality for the general linear regression model (1.1).…”

Section: Equivalence Relationsmentioning

confidence: 99%

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