{"paper":{"title":"Robust estimation of U-statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Emilien Joly, G\\'abor Lugosi","submitted_at":"2015-04-17T17:13:39Z","abstract_excerpt":"An important part of the legacy of Evarist Gin\\'e is his fundamental contributions to our understanding of $U$-statistics and $U$-processes. In this paper we discuss the estimation of the mean of multivariate functions in case of possibly heavy-tailed distributions. In such situations, reliable estimates of the mean cannot be obtained by usual $U$-statistics. We introduce a new estimator, based on the so-called median-of-means technique. We develop performance bounds for this new estimator that generalizes an estimate of Arcones and Gin\\'e (1993), showing that the new estimator performs, under"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04580","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}