Asymptotically Nonparametric Inference: An Alternative Approach to Linear Models

Abstract

As an alternative to the standard analysis of variance, procedures are developed for linear models with several observations per cell which are asymptotically distribution-free and whose asymptotic efficiency relative to the standard procedures is the same as that of the Wilcoxon test relative to Student's $t$-test. Specific procedures discussed are (i) tests of linear hypotheses, (ii) confidence intervals for any contrast, (iii) simultaneous intervals for all contrasts.