0000000000341535

AUTHOR

Rainer Schwabe

showing 3 related works from this author

Optimal designs for a one-way layout with covariates

2000

Abstract For the general class of Φ q -criteria optimal designs are characterized which reflect the inherent symmetry in a one-way layout with covariates. In particular, the eigenvalues of the covariance matrices are related to those in suitably chosen marginal models depending on the underlying interaction structure.

Statistics and ProbabilityOptimal designMathematical optimizationClass (set theory)Applied MathematicsMathematicsofComputing_NUMERICALANALYSISMarginal modelCovarianceSymmetry (physics)CovariateStatistics Probability and UncertaintyAdditive modelEigenvalues and eigenvectorsMathematicsJournal of Statistical Planning and Inference
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Efficiency Bounds for Product Designs in Linear Models

1999

We provide lower efficiency bounds for the best product design for an additive multifactor linear model. The A-optimality criterion is used to demonstrate that out bounds are better than the conventional bounds. Applications to other criteria, such as IMSE (integrated mean squared error) criterion are also indicated. In all the cases, the best product design appears to perform better when there are more levels in each factor but decreases when more factors are included. Explicit efficiency formulas for non-additive models are also constructed.

Statistics and ProbabilityOptimal designProduct designMean squared errorLinear modelMarginal modelsymbols.namesakeProduct (mathematics)StatisticssymbolsApplied mathematicsFisher informationAdditive modelMathematicsAnnals of the Institute of Statistical Mathematics
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Lattices and dual lattices in optimal experimental design for Fourier models

1998

Number-theoretic lattices, used in integration theory, are studied from the viewpoint of the design and analysis of experiments. For certain Fourier regression models lattices are optimal as experimental designs because they produce orthogonal information matrices. When the Fourier model is restricted, that is a special subset of the full factorial (cross-spectral) model is used, there is a difficult inversion problem to find generators for an optimal design for the given model. Asymptotic results are derived for certain models as the dimension of the space goes to infinity. These can be thought of as a complexity theory connecting designs and models or as special type of Nyquist sampling t…

Statistics and ProbabilityOptimal designDiscrete mathematicsFactorialApplied MathematicsDesign of experimentsInversion (meteorology)Regression analysisComputational Mathematicssymbols.namesakeFourier transformComputational Theory and MathematicsLattice (order)symbolsApplied mathematicsNyquist–Shannon sampling theoremMathematicsComputational Statistics & Data Analysis
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