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 $\theta = \sum c_i\xi_i$.