Asymptotic Confidence Intervals Based on M-procedures in One- and Two-sample Models

Abstract

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. Furthermore although the symmetry of the underlying distribution is needed in the asymptotic theory of Huber's M-estimators, the proposed procedures do not demand the symmetry in the two-sample model. The asymptotic efficiency of the proposed confidence intervals is given by a numerical integration.