| Titre : | About The Nonparametric Estimation with K-Nearest Neighbors for Functional Data |
| Auteurs : | Madani . F, Directeur de thèse ; Zahira .Arabi, Auteur |
| Type de document : | texte imprimé |
| Format : | 103 p. / fig.;tab. / 27 cm. |
| Note générale : | Bibliographie |
| Langues: | Anglais |
| Langues originales: | Anglais |
| Mots-clés: | Mathématique ; About The Nonparametric Estimation ; K-Nearest Neighbors ; Functional Data |
| Résumé : | We present in this work a few convergence results of the k-NN kernel estimator in nonparametric regression for the functional, real and vector data. Also we illustrate How the k-NN algorithm work in R and in our daily life.For onparametric estimation, we showed some of many asymptotic property that this method gives; the almost complete pointwise convergence of this estimator and we established its rate of convergence. We remarked that this rate is similar to the rate of convergence of Nadaraya-Watson type kernel estimator (optimal rates are the same). So, from a theoretical point of view, these two methods have the same asymptotical properties and we do not have any loss of effectiveness. This is in concordance with the knowledge in multivariate (unfunctional) nonparametric situations for which methods are known to achieve optimal rates of convergence [40],however, the infinite dimension of the data makes the use of the k-NN method more natural. The real interest of the k-NN method appears on practical examples. The fact that the smoothing parameter k takes its values in a discrete set makes things more simple from an implementation points of view. Moreover, we make example in finance to compare between the k-NN method and the logistic regression, and also we showed in examples that k-NN method takes into account the local structure of the data and gives better predictions when the data are heterogeneously concen-trated. |
| Note de contenu : |
1 k-Nearest Neighbors: State of the Art 2 ThekNN method for functional data 3 Simulation using the k nearest neighbors method |
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