The depth of multivariate data can be used to construct weighted means as robust estimators of location. The use of projection depth leads to the Stahel-Donoho estimator as a special case. In contrast to maximal depth estimators, the depth-weighted means are shown to be asymptotically normal under appropriate conditions met by depth functions commonly used in the current literature. We also confirm through a finite-sample study that the Stahel-Donoho estimator achieves a desirable balance between robustness and efficiency at Gaussian models.
Introduction.Depth functions for multivariate data have piqued the interest of researchers in robust and nonparametric statistics for quite some time. A number of data depth measures, including the half-space depth of Tukey (1975), the simplicial depth of Liu (1990) and the projection depth discussed in Liu (1992) and Zuo and Serfling (2000a), have been proposed and discussed for outlier detection, data ranking and robust estimation. General discussions of the properties of data depth can be found in Liu and Singh (1993), He and Wang (1997), Rousseeuw and Hubert (1999) and Zuo and Serfling (2000b). More extensive studies of Tukey's half-space depth and the associated location estimators were made by Donoho and Gasko (1992) on robustness and Massé (1999) on asymptotics. The Stahel-Donoho estimator [Stahel (1981) and Donoho (1982)], a location estimator based on projection depth, has been studied by Tyler (1994) on robustness and by Maronna and Yohai (1995) on asymptotics. The limiting distribution of the Stahel-Donoho estimator has not been worked out, notwithstanding.The present paper focuses on the asymptotic behavior of the depth-weighted L-type location estimators. Following Liu (1990) and Liu, Parelius and Singh (1999), we shall call them DL-estimators of location. We give sufficient conditions
Understanding the mechanism of protective antibody recognition against highly pathogenic avian influenza A virus H5N1 in humans is critical for the development of effective therapies and vaccines. Here we report the crystal structure of three H5-specific human monoclonal antibodies bound to the globular head of hemagglutinin (HA) with distinct epitope specificities, neutralization potencies and breadth. A structural and functional analysis of these epitopes combined with those reported elsewhere identifies four major vulnerable sites on the globular head of H5N1 HA. Chimeric and vulnerable site-specific mutant pseudoviruses are generated to delineate broad neutralization specificities of convalescent sera from two individuals who recovered from the infection with H5N1 virus. Our results show that the four vulnerable sites on the globular head rather than the stem region are the major neutralizing targets, suggesting that during natural H5N1 infection neutralizing antibodies against the globular head work in concert to provide protective antibody-mediated immunity.
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