Result · DS-CLASSICAL-DESIGN-THEORY

Classical design theory already covers nuisance parameters

Establishedpublication: published

Meaning

Established optimal-design theory supplies the background for profiled determinant criteria.

Statement

Classical optimal-design theory supplies Ds/subset criteria, Schur-complement formulations, sensitivity/equivalence theorems, and nuisance-parameter tools.

Where it stops

The design feasible set differs from hard score-space partitioning.

Closest prior work

Wynn (1972)Results in the Theory and Construction of D-Optimum Experimental Designs
Whittle (1973)Some General Points in the Theory of Optimal Experimental Design
Näther, Reinsch (1981)D_s-optimality and Whittle's equivalence theorem
Kiefer (1974)General Equivalence Theory for Optimum Designs (Approximate Theory)
Silvey, Titterington (1973)A Geometric Approach to Optimal Design Theory

Nearest prior work

Kiefer, Wolfowitz (1960)The Equivalence of Two Extremum Problems
Wynn (1970)The Sequential Generation of D-Optimum Experimental Designs
Silvey, Titterington, Torsney (1978)An Algorithm for Optimal Designs on a Design Space

Relationships

Local graph

Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

Proof

DS1. Classical $D_s$ design theory

Wynn, Whittle, Näther–Reinsch, Kiefer/general equivalence theory provide classical subset/nuisance-parameter optimal design, sensitivity, and singular-case tools. They do not directly solve the quantizer feasible set.

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