Optimal designs and large-sample tests for linear hypotheses

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

doi:10.1093/biomet/62.1.71

Optimal designs and large-sample tests for linear hypotheses

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

Arizona State University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 language	English (US)
Pages (from-to)	71-78
Number of pages	8
Journal	Biometrika
Volume	62
Issue number	1
DOIs	https://doi.org/10.1093/biomet/62.1.71
State	Published - Apr 1975

Keywords

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

ASJC Scopus subject areas

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

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10.1093/biomet/62.1.71

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title = "Optimal designs and large-sample tests for linear hypotheses",

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, Scheff{\'e}'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.",

keywords = "Berry-Ess{\'e}en bounds, Central limit theory, Dunnett's procedure, Linear models, Optimal designs and robustness, Scheff{\'e}'s projections",

author = "Jensen, {D. R.} and Mayer, {L. S.} and Mayers, {R. H.}",

note = "Funding Information: Financial support was provided by the U.S. Office of Naval Research for the first third authors, and by the National Institute of Mental Health for the second author.",

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T1 - Optimal designs and large-sample tests for linear hypotheses

AU - Jensen, D. R.

AU - Mayer, L. S.

AU - Mayers, R. H.

N1 - Funding Information: Financial support was provided by the U.S. Office of Naval Research for the first third authors, and by the National Institute of Mental Health for the second author.

PY - 1975/4

Y1 - 1975/4

N2 - 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.

AB - 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.

KW - Berry-Esséen bounds

KW - Central limit theory

KW - Dunnett's procedure

KW - Linear models

KW - Optimal designs and robustness

KW - Scheffé's projections

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JO - Biometrika

JF - Biometrika

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ER -

Optimal designs and large-sample tests for linear hypotheses

Abstract

Keywords

ASJC Scopus subject areas

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