6533b862fe1ef96bd12c6193
RESEARCH PRODUCT
Lattices and dual lattices in optimal experimental design for Fourier models
R. A. BatesEva RiccomagnoHenry P. WynnRainer Schwabesubject
Statistics and ProbabilityOptimal designDiscrete mathematicsFactorialApplied MathematicsDesign of experimentsInversion (meteorology)Regression analysisComputational Mathematicssymbols.namesakeFourier transformComputational Theory and MathematicsLattice (order)symbolsApplied mathematicsNyquist–Shannon sampling theoremMathematicsdescription
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 theory.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1998-09-01 | Computational Statistics & Data Analysis |