The Annals of Mathematical Statistics

Robust Procedures for Some Linear Models with one Observation per Cell

Kjell Doksum

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Abstract

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 $\theta = \sum c_i\xi_i$.

Article information

Source
Ann. Math. Statist., Volume 38, Number 3 (1967), 878-883.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177698881

Digital Object Identifier
doi:10.1214/aoms/1177698881

Mathematical Reviews number (MathSciNet)
MR210256

Zentralblatt MATH identifier
0149.15602

JSTOR
links.jstor.org

Citation

Doksum, Kjell. Robust Procedures for Some Linear Models with one Observation per Cell. Ann. Math. Statist. 38 (1967), no. 3, 878--883. doi:10.1214/aoms/1177698881. https://projecteuclid.org/euclid.aoms/1177698881


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