{"paper":{"title":"Pointwise Adaptive M-estimation in Nonparametric Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Micha\\\"el Chichignoud","submitted_at":"2011-05-09T12:00:06Z","abstract_excerpt":"This paper deals with the nonparametric estimation in heteroscedastic regression $ Y_i=f(X_i)+\\xi_i, \\: i=1,...,n $, with incomplete information, i.e. each real random variable $ \\xi_i $ has a density $ g_{i} $ which is unknown to the statistician. The aim is to estimate the regression function $ f $ at a given point. Using a local polynomial fitting from M-estimator denoted $ \\hat f^h $ and applying Lepski's procedure for the bandwidth selection, we construct an estimator $ \\hat f^{\\hat h} $ which is adaptive over the collection of isotropic H\\\"{o}lder classes. In particular, we establish new"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1646","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"}