Estimating minimum effect with outlier selection

نویسندگان

چکیده

We introduce one-sided versions of Huber’s contamination model, in which corrupted samples tend to take larger values than uncorrupted ones. Two intertwined problems are addressed: estimation the mean (minimum effect) and selection (outliers). Regarding minimum effect, we derive minimax risks estimators that adaptive with respect unknown number contaminations. The optimal convergence rates differ from ones classical Huber model. This fact uncovers effect structural assumption As for problem selecting outliers, formulate a multiple testing framework location scaling null hypotheses unknown. rigorously prove estimating hypothesis while maintaining theoretical guarantee on amount falsely selected outliers is possible, both through false discovery rate (FDR) post hoc bounds. by-product, address long-standing open issue FDR control under equi-correlation, reinforces interest removing dependency such setting.

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ژورنال

عنوان ژورنال: Annals of Statistics

سال: 2021

ISSN: ['0090-5364', '2168-8966']

DOI: https://doi.org/10.1214/20-aos1956