Multivariate statistical theory based on robust statistics

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Statistical estimation procedures are proposed based on studentized robust statistics for location parameters in two-way layouts with interaction. Large sample properties of their 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. 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.Asymptotic confidence intervals of location parameters are proposed in one-and two-sample models. These are robust procedures based on scale-invariant M-statistics. The one-sample procedures have the same robustness as Huber's M-estimators. The asymptotic efficiency of the proposed confidence intervals is given by a numerical integration.In my book entitled "Tokei Kagaku", parametorics, nonparametorics and semiparametorics are discussed. The way of making a selection from the three procedures is stated based on the search of the undelying distribution and goodness of fit tests.