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A universal robustification procedure

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arxiv 2206.06998 v5 pith:W67X4C3T submitted 2022-06-14 math.ST math.PRstat.TH

Riccardo Passeggeri , Nancy Reid This is my paper · ORCID
classification math.STmath.PRstat.TH
keywords estimatorprocedureasymptoticallydistributionnormalwhosearbitrarycontamination
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We develop a procedure that transforms any asymptotically normal estimator into an asymptotically normal estimator whose distribution is robust to arbitrary data contamination. More generally, our procedure transforms any estimator whose asymptotic distribution has positive and continuous density at the origin into an asymptotically normal estimator whose distribution is robust to arbitrary contamination. In developing such a procedure we prove new general properties of componentwise and geometric quantiles in both finite and infinite dimensions.

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Cited by 1 Pith paper

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  1. Spatial depth characterizes probability measures

    math.ST 2026-07 accept novelty 8.0 of 10

    Spatial depth (and the spatial cdf/quantiles) fully characterize Borel probability measures on separable Hilbert spaces, finite- or infinite-dimensional.

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