J. Japan Statist. Soc., Vol. 34 (No. 1), pp. 87-99, 2004

Asymptotic confidence intervals based on M-procedures in one- and two-sample models

Taka-aki Shiraishi

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.

Key words and phrases: Asymptotics, confidence region, M-estimators, robustness.

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