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July, 1974 On a Measure of Aliasing Due to Fitting an Incomplete Model
A. Hedayat, B. L. Raktoe, W. T. Federer
Ann. Statist. 2(4): 650-660 (July, 1974). DOI: 10.1214/aos/1176342754

Abstract

This paper proposes and develops a method for selecting a design to estimate a set of linear parametric functions in cases wherein the adequacy of the preliminary linear model is in doubt. The proposed method relies on the norm of the aliasing matrix. If the expected value of the estimator $\hat{\psi}$ of a set of linear functions $\psi = L_1\theta_1$ using a design $\Gamma$, under the true model is $E\lbrack\hat{\psi}\rbrack = \psi + A_\Gamma \theta_2$, then the norm $\|A_\Gamma\| =$ (trace $A_\Gamma' A_\Gamma)^{\frac{1}{2}}$ is presented as a measure for use in determining "alias balance" and "alias goodness." Therefore, $\|A_\Gamma\|$ may be used in the selection of a design for experimentation, and its behaviour under various operations is discussed. Some theorems concerning aliases of rank equivalent and complementary designs in certain settings are obtained.

Citation

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A. Hedayat. B. L. Raktoe. W. T. Federer. "On a Measure of Aliasing Due to Fitting an Incomplete Model." Ann. Statist. 2 (4) 650 - 660, July, 1974. https://doi.org/10.1214/aos/1176342754

Information

Published: July, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0286.62057
MathSciNet: MR433758
Digital Object Identifier: 10.1214/aos/1176342754

Keywords: Adequacy of a model , alias balance , alias goodness , alias measure , factorial experiment , fractional replicate

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 4 • July, 1974
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