Efficiencies of some small second-order designs

Jensen, D. R.

doi:10.1016/0167-7152(94)90135-x

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2011

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Cited by 2 publications

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“…The run size of these designs increases rapidly as the number of factors k increases, however. For central composite design, efforts have been made to reduce the run size (see, for example, Draper, 1985;Draper andLin, 1990, 1996;Jensen, 1994). For Box-Behnken design, little is known on reducing the run size.…”

Section: Introductionmentioning

confidence: 99%

Small Box–Behnken design

Zhang

Lin

2011

Statistics & Probability Letters

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Section: Introductionmentioning

confidence: 99%

Small Box–Behnken design

Zhang

Lin

2011

Statistics & Probability Letters

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Determinant Efficiencies in Ill‐Conditioned Models

Jensen

2011

Journal of Probability and Statistics

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The canonical correlations between subsets of OLS estimators are identified with design linkage parameters between their regressors. Known collinearity indices are extended to encompass angles between each regressor vector and remaining vectors. One such angle quantifies the collinearity of regressors with the intercept, of concern in the corruption of all estimates due to ill-conditioning. Matrix identities factorize a determinant in terms of principal subdeterminants and the canonical Vector Alienation Coefficients between subset estimators-by duality, the Alienation Coefficients between subsets of regressors. These identities figure in the study of D and D s as determinant efficiencies for estimators and their subsets, specifically, D s -efficiencies for the constant, linear, pure quadratic, and interactive coefficients in eight known small second-order designs. Studies on D-and D s -efficiencies confirm that designs are seldom efficient for both. Determinant identities demonstrate the propensity for D s -inefficient subsets to be masked through near collinearities in overall D-efficient designs.

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Efficiencies of some small second-order designs

Cited by 2 publications

References 25 publications

Small Box–Behnken design

Small Box–Behnken design

Determinant Efficiencies in Ill‐Conditioned Models

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