High-probability minimax lower bounds

arXiv:2406.13447v1 Announce Type: cross
Abstract: The minimax risk is often considered as a gold standard against which we can compare specific statistical procedures. Nevertheless, as has been observed recently in robust and heavy-tailed estimation problems, the inherent reduction of the (random) loss to its expectation may entail a significant loss of information regarding its tail behaviour. In an attempt to avoid such a loss, we introduce the notion of a minimax quantile, and seek to articulate its dependence on the …

abstract arxiv cs.it cs.lg gold information loss math.it math.st minimax probability random risk robust standard statistical stat.ml stat.th type