ROBUST ESTIMATES OF LOCATION PARAMETERS IN TWO-WAY LAYOUTS WITH INTERACTION

Abstract

Statistical estimation procedures are proposed based on studentized robust statistics for location parameters in two-way layouts with interaction. Large sample properties of these procedures as the cell size tends to infinity are investigated. Although Fisher's consistency is assumed in the theory of M-estimators, it is not needed in this paper. 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, it can be seen that the proposed estimators are more efficient than least squares estimators except for the case where the underlying distribution is normal.