On the Consistency of Kernel Classification Rule for Functional Random Field
[Sur la consistance de la règle de classification du noyau pour le champ aléatoire fonctionnel]
Journal de la société française de statistique, Tome 159 (2018) no. 1, pp. 68-87.

Nous considérons la règle de la fenêtre mobile pour classifier des données fonctionnelles spatialement dépendantes. Nous étudions les propriétés asymptotiques de cette règle de classification non paramétrique basée sur des données d’apprentissage tirées d’un champ aléatoire α ou β - mélangeant à valeurs en espace de dimension infinie. Nous étendons les résultats de Younso (2017a) concernant la consistance et la consistance forte au cas spatialement dépendant sous des hypothèses non restrictives. Nous proposons un critère pour choisir le paramètre de lissage et nous considérons l’application de notre approche sur des données simulées.

We consider the classical moving window rule of classification for functional spatially dependent data. We investigate asymptotic properties of this nonparametric classification rule based on training data drawn from α or β - mixing random field taking values in infinite-dimensional space. We extend the results of Younso (2017a) concerning both the consistency and the strong consistency of the moving window classifier to the spatially dependent case under mild assumptions. We propose a method for bandwidth selection and we conduct some simulation studies.

Mots clés : Règle de Bayes, données d’apprentissage, règle de fenêtre mobile, champ aléatoire, paramètre de lissage, consistance
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Younso, Ahmad. On the Consistency of Kernel Classification Rule for Functional Random Field. Journal de la société française de statistique, Tome 159 (2018) no. 1, pp. 68-87. http://www.numdam.org/item/JSFS_2018__159_1_68_0/

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