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June, 1967 Robust Procedures for Some Linear Models with one Observation per Cell
Kjell Doksum
Ann. Math. Statist. 38(3): 878-883 (June, 1967). DOI: 10.1214/aoms/1177698881


For block designs with one observation per cell, the model often used is the linear model in which the observations $X_{i\alpha} (i = 1, \cdots, r; \alpha = 1, \cdots, n)$ can be written \begin{equation*}\tag{1.1} X_{i\alpha} = v + \xi_i + \mu_\alpha + Y_{i\alpha} (\sum \xi_i = \sum \mu_\alpha = 0)\end{equation*} where the $\xi's$ are the parameters of interest (treatment effect) the $\mu's$ are nuisance parameters (block effect), and the $Y's$ are independent with common continuous distribution $F$. The purpose of this note is to discuss some new robust test statistics (e.g. 2.14 and 2.16) of the null-hypothesis $H_0 : \xi_1 = \xi_2 = \cdots = \xi_r$, and to discuss a new robust estimate (3.3) of the contrast $\theta = \sum c_i\xi_i$.


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Kjell Doksum. "Robust Procedures for Some Linear Models with one Observation per Cell." Ann. Math. Statist. 38 (3) 878 - 883, June, 1967.


Published: June, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0149.15602
MathSciNet: MR210256
Digital Object Identifier: 10.1214/aoms/1177698881

Rights: Copyright © 1967 Institute of Mathematical Statistics

Vol.38 • No. 3 • June, 1967
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