## The Annals of Mathematical Statistics

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

### Robust Procedures for Some Linear Models with one Observation per Cell

#### 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