Optimal designs and large-sample tests for linear hypotheses

D. R. Jensen, L. S. Mayer, R. H. Mayers

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Moment conditions beyond those required for Gauss-Markov estimation are shown to yield error bounds on normal-theory approximations to type I error probabilities and confidence coefficients associated with variance ratio tests, Scheffé's (1953) bounds, and Dunnett's (1955) procedure for comparing k treatments with a control. These bounds depend on the experimental design. The error-minimizing designs are characterized and shown to be orthogonal.

Original languageEnglish (US)
Pages (from-to)71-78
Number of pages8
JournalBiometrika
Volume62
Issue number1
DOIs
StatePublished - Apr 1975
Externally publishedYes

Fingerprint

Linear Hypothesis
Research Design
experimental design
Ratio test
Variance Ratio
Approximation theory
Moment Conditions
Type I error
Approximation Theory
Error Probability
Experimental design
Design of experiments
Error Bounds
Gauss
Confidence
testing
sampling
Coefficient
Optimal design
Design

Keywords

  • Berry-Esséen bounds
  • Central limit theory
  • Dunnett's procedure
  • Linear models
  • Optimal designs and robustness
  • Scheffé's projections

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Mathematics(all)
  • Statistics and Probability
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)

Cite this

Optimal designs and large-sample tests for linear hypotheses. / Jensen, D. R.; Mayer, L. S.; Mayers, R. H.

In: Biometrika, Vol. 62, No. 1, 04.1975, p. 71-78.

Research output: Contribution to journalArticle

Jensen, DR, Mayer, LS & Mayers, RH 1975, 'Optimal designs and large-sample tests for linear hypotheses', Biometrika, vol. 62, no. 1, pp. 71-78. https://doi.org/10.1093/biomet/62.1.71
Jensen, D. R. ; Mayer, L. S. ; Mayers, R. H. / Optimal designs and large-sample tests for linear hypotheses. In: Biometrika. 1975 ; Vol. 62, No. 1. pp. 71-78.
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