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Within the considered mathematical framework, we recover classical results in functional analysis, such as a Poincar\u00e9-type inequality. This, in turn, enables us to uplift, to the present setting, the theory of some fundamental penalized likelihood methods. Specifically, we present two important classes of statistical models: nonparametric regression and nonparametric density estimation, here defined for data observed over graphs. We derive theoretical results regarding the well-posedness of the associated estimation problems and the consistency of the estimators. We also demonstrate the performance of the defined estimators with respect to state-of-the-art alternatives.<\/jats:p>","DOI":"10.1093\/biomet\/asag029","type":"journal-article","created":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T11:39:33Z","timestamp":1775907573000},"source":"Crossref","is-referenced-by-count":3,"title":["Nonparametric estimators over metric graphs"],"prefix":"10.1093","volume":"113","author":[{"given":"Aldo","family":"Clemente","sequence":"first","affiliation":[{"name":"MOX - Department of Mathematics, Politecnico di Milano , Piazza Leonardo da Vinci 32 , 20133 Milano, \u00a0 aldo.clemente@polimi.it","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eleonora","family":"Arnone","sequence":"additional","affiliation":[{"name":"Department of Management, Universit\u00e0 degli Studi di Torino , Via Giuseppe Verdi 8 , 10124 Torino, \u00a0 eleonora.arnone@unito.it","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jorge","family":"Mateu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universitat Jaume I , Avinguda de Vicent Sos Baynat , 12006 Castell\u00f3 de la Plana, \u00a0 mateu@uji.es","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4951-9239","authenticated-orcid":false,"given":"Laura M","family":"Sangalli","sequence":"additional","affiliation":[{"name":"MOX - Department of Mathematics, Politecnico di Milano , Piazza Leonardo da Vinci 32 , 20133 Milano,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,4,15]]},"reference":[{"key":"2026080308114429700_asag029-B1","doi-asserted-by":"crossref","first-page":"2478","DOI":"10.1214\/19-AOS1896","article-title":"Isotropic covariance functions on graphs and their edges","volume":"48","author":"Anderes","year":"2020","journal-title":"Ann. 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