caa a22 4500 475793293 CHVBK 20180406123716.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/s001840000062 doi (NATIONALLICENCE)springer-10.1007/s001840000062 Zuo Yijun aut Finite sample tail behavior of the multivariate trimmed mean based on Tukey-Donoho halfspace depth [Elektronische Daten] [Yijun Zuo] Abstract.: Finite sample tail behavior of the Tukey-Donoho halfspace depth based multivariate trimmed mean is investigated with respect to a tail performance measure. It turns out that the tails of the sampling distribution of the α-depth-trimmed mean approach zero at least ⌊αn⌋ times as fast as the tails of the underlying population distribution and could be n−⌊αn⌋+ 1 times as fast. In addition, there is an intimate relationship among the tail behavior, the halfspace depth, and the finite sample breakdown point of the estimator. It is shown that the lower tail performance bound of the depth based trimmed mean is essentially the same as its halfspace depth and the breakdown point. This finding offers a new insight into the notion of the halfspace depth and extends the important role of the tail behavior as a quantitative assessment of robustness in the regression (He, Jurečková, Koenker and Portnoy (1990)) and the univariate location settings (Jurečková (1981)) to the multivariate location setting. Springer-Verlag Berlin Heidelberg, 2000 AMS 1991 Classification: Primary 62F35 nationallicence Secondary 62G35, 62H12 nationallicence Key words: Depth-trimmed mean, tail behavior, halfspace depth, robustness, breakdown point nationallicence https://doi.org/10.1007/s001840000062 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001840000062 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zuo Yijun aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer