On Some Optimum Nonparametric Procedures in Two-Way Layouts

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Abstract
Some optimum nonparametric procedures for estimating and testing contrasts in two-way layouts are proposed and studied. These procedures are based on the Chernoff-Savage [4] type of rank order statistics which include the Wilcoxon and normal scores statistics among others. In the first three sections, the properties of the proposed point estimators of contrasts, such as symmetry, invariance and asymptotic normality, are studied and their asymptotic relative efficiencies with respect to the corresponding least-squares estimators are obtained. In particular, it is shown that the procedures based on the normal scores statistics are asymptotically at least as efficient as the corresponding procedures based on the method of least squares, whatever be parent cumulative distribution functions. In sections 4 and 5, the corresponding problems of testing and confidence intervals are discussed, and generalized to two-way layouts with several observations per cell.

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