Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 2, 161--177



YIJUN ZUO, Arizona State University, Tempe

SUMMARY. A notion of monotonicity of multivariate location estimators is introduced. The relationships between this notion and other existing notions are discussed. Finite sample breakdown point properties of multivariate monotone location estimators are investigated. It turns out that the breakdown points of typical multivariate monotone location estimators are independent of the configuration of underlying observations and play an important role in the characterization of these estimators. Tail behavior of multivariate monotone location estimators is explored with respect to a finite sample ``tail behavior'' measure. Relationships among monotonicity, equivariance and high breakdown point of multivariate location estimators are discussed.

AMS (1991) subject classification. Primary 62F10, 62H12; secondary 62F35, 62G05.

Key words and phrases. Multivariate location estimators, monotonicity, breakdown point, tail behavior, equivariance.

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