@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00337058v3> a dcat:Dataset ;
    dct:description """
              The performance of cross-validation (CV) is analyzed in two contexts: (i) risk estimation and (ii) model selection in the density estimation framework. The main focus is given to one CV algorithm called leave-$p$-out (Lpo), where $p$ denotes the cardinality of the test set. Closed-form expressions are settled for the Lpo estimator of the risk of projection estimators, which makes V-fold cross-validation completely useless. From a theoretical point of view, these closed-form expressions enable to study the Lpo performances in terms of risk estimation. For instance, the optimality of leave-one-out (Loo), that is Lpo with $p=1$, is proved among CV procedures. Two model selection frameworks are also considered: estimation, as opposed to identification. Unlike risk estimation, Loo is proved to be suboptimal as a model selection procedure. In the estimation framework with finite sample size $n$, optimality is achieved for $p$ large enough (with $p/n =o(1)$) to balance overfitting. A link is also identified between the optimal $p$ and the structure of the model collection. These theoretical results are strongly supported by simulation experiments. When performing identification, model consistency is also proved for Lpo with $p/n\\to 1$ as $n\\to +\\infty$.
            """ ;
    dct:identifier "hal-00337058" ;
    dct:issued "2026-05-23T00:40:07.615721"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-23T00:40:07.615726"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Optimal cross-validation in density estimation" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00337058v3/resource/55ef13a8-c86c-4443-9451-b90fce2a6b7b> ;
    dcat:keyword "62g09--62g07--62e17",
        "concentration-inequalities",
        "cross-validation",
        "density-estimation",
        "infoeu-reposemanticspreprint",
        "leave-p-out",
        "mathmath-stmathematics-mathstatistics-mathst",
        "model-selection",
        "oracle-inequality",
        "preprints-working-papers-",
        "projection-estimators",
        "resampling",
        "risk-estimation",
        "statthstatistics-statstatistics-theory-statth" ;
    dcat:landingPage <https://hal.science/hal-00337058> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00337058v3/resource/55ef13a8-c86c-4443-9451-b90fce2a6b7b> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-23T00:40:07.635378"^^xsd:dateTime ;
    dct:modified "2026-05-23T00:40:07.579163"^^xsd:dateTime ;
    dct:title "Optimal cross-validation in density estimation" ;
    dcat:accessURL <https://hal.science/hal-00337058> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .

<https://hal.science/hal-00337058> a foaf:Document .