{"paper":{"title":"A Note on Exponential Inequalities in Hilbert Spaces for Spatial Processes with Applications to the Functional Kernel Regression Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Johannes T. N. Krebs","submitted_at":"2017-08-28T19:55:47Z","abstract_excerpt":"In this manuscript we present exponential inequalities for spatial lattice processes which take values in a separable Hilbert space and satisfy certain dependence conditions. We consider two types of dependence: spatial data under $\\alpha$-mixing conditions and spatial data which satisfies a weak dependence condition introduced by Dedecker and Prieur [2005]. We demonstrate their usefulness in the functional kernel regression model of Ferraty and Vieu [2004] where we study uniform consistency properties of the estimated regression operator on increasing subsets of the underlying function space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08505","kind":"arxiv","version":2},"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"}