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June, 1964 Estimates of Effects for Fractional Replicates
K. S. Banerjee, W. T. Federer
Ann. Math. Statist. 35(2): 711-715 (June, 1964). DOI: 10.1214/aoms/1177703568


Given any fraction of a factorial experiment in which the treatments either occur zero or one time, previous results were obtained on augmentation of the treatment design matrix, $X$, such that the product of the transpose and of the augmented matrix, $X_1 = \lbrack X'\vdots X'\lambda\rbrack'$, resulted in a diagonal matrix, and on a transformation of $X_1$ to another matrix $X_2 = FX_1$. In the present paper results are obtained on the evaluation of the variances of estimated effects under augmentation, on the existence and evaluation of $F$ and $\lambda$, on the determination of aliases of effects, and on the calculation of inverses for $\lbrack X'X\rbrack$ and for the information matrix $\lbrack X'_{22}X_{22}\rbrack$ for the deleted treatments.


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K. S. Banerjee. W. T. Federer. "Estimates of Effects for Fractional Replicates." Ann. Math. Statist. 35 (2) 711 - 715, June, 1964.


Published: June, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0125.37503
MathSciNet: MR161411
Digital Object Identifier: 10.1214/aoms/1177703568

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 2 • June, 1964
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