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Optimal Design An Introduction to the Theory for Parameter Estimation

Prior to the 1970's a substantial literature had accumulated on the theory of optimal design, particularly of optimal linear regression design. To a certain extent the study of the subject had been piecemeal, different criteria of optimality having been studied separately. Also to a certain ext...

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Bibliographic Details
Main Author: Silvey, S.
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1980, 1980
Edition:1st ed. 1980
Series:Ettore Majorana International Science Series, Physical Sciences
Subjects:
Humanities And Social Sciences
Humanities
Social Sciences
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Introduction
  • 1.1 Historical note
  • 1.2 The general problem
  • 1.3–1.6 Examples
  • 1.7 Discriminating among models
  • 2 Linear theory
  • 2.1 Definition
  • 2.2 Design criteria
  • 2.3 A property of criterion functions
  • 2.4 Approximate theory
  • 3 Approximate theory for linear regression design
  • 3.1 The general problem
  • 3.2 The set of information matrices
  • 3.3 The criterion function
  • 3.4 The solution set of design measures
  • 3.5 Directional derivatives
  • 3.6,3.7 Basic theorems
  • 3.8 Example: quadratic regression with a single control variable
  • 3.9 Theorem: equivalence of D-and G-optimality
  • 3.10 Corollary
  • 3.11–3.12 Discussion
  • 3.13 Optimal design measures with singular information matrices
  • 4 Algorithms
  • 4.1 Introduction
  • 4.2 Design measure algorithms
  • 4.3 The V-algorithm for D-optimality
  • 4.4 An example of the use of the W-algorithm
  • 4.5 General comments
  • 4.6 Convergence considerations
  • 4.7 Review
  • 4.8 N-observation designs
  • 5 Approximate theory—particular criteria
  • 5.1 D-optimality
  • 5.2 DA- and DS-optimality
  • 5.3 A linear criterion function
  • 5.4 c-optimality
  • 5.5 Examples
  • 5.6 Other criteria
  • 6 Non-linear problems
  • 6.1 Introduction
  • 6.2–6.6 Examples
  • 7 Sequential designs
  • 7.1 Objective
  • 7.2 An alternative method
  • 7.3 Convergence considerations
  • 7.4 Inference from sequentially constructed designs
  • Appenddix
  • A.1 Concavity results
  • A.2 Carathéodory’s Theorem
  • A.3 Differentiability
  • A.4 Lagrangian theory: duality

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