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• W2029930544 abstract "L p –norm weighted depth functions are introduced and the local and global robustness of these weighted L p –depth functions and their induced multivariate medians are investigated via influence function and finite sample breakdown point. To study the global robustness of depth functions, a notion of finite sample breakdown point is introduced. The weighted L p –depth functions turn out to have the same low breakdown point as some other popular depth functions. Their influence functions are also unbounded. On the other hand, the weighted L p –depth induced medians are globally robust with the highest possible breakdown point for any reasonable estimator. The weighted L p –medians are also locally robust with bounded influence functions for suitable weight functions. Unlike other existing depth functions and multivariate medians, the weighted L p depth and medians are easy to calculate in high dimensions. The price for this advantage is the lack of affine invariance and equivariance of the weighted L p depth and medians, respectively." @default.
• W2029930544 created "2016-06-24" @default.
• W2029930544 creator A5077086313 @default.
• W2029930544 date "2004-05-01" @default.
• W2029930544 modified "2023-10-16" @default.
• W2029930544 title "Robustness of weighted L p ?depth and L p ?median" @default.
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• W2029930544 doi "https://doi.org/10.1007/s101820400169" @default.
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