Abstract
Multiresponse experiments in two-way layouts with interaction, having equal number of observations per cell, are considered. Statistical procedures of the test, estimation and confidence region, based on M-statistics, for interactions and main effects in the models are proposed. Large sample properties of their procedures as the cell size tends to infinity are investigated. The usual assumption of M-procedures that the underlying distribution is diagonally symmetric is not needed. For the univariate case, it is found that the asymptotic relative efficiencies (ARE's) of the proposed procedures relative to classical procedures agree with the classical ARE-results of Huber's one sample M-estimator relative to the sample mean. By simulation studies, the goodness of the x2-approximate for the significance points of the M-tests is investigated, and it can be seen that the M-estimators are robust with respect to the contaminated distribution. Furthermore M-procedures for two-way MANOVA without interaction are discussed briefly.
