On the Estimation of the Density of a Directional Data Stream

Amiri, Aboubacar; Thiam, Baba; Verdebout, Thomas

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1111/sjos.12252

Title :

On the Estimation of the Density of a Directional Data Stream

Author(s) :

Amiri, Aboubacar [Auteur]
Lille économie management - UMR 9221 [LEM]
Thiam, Baba [Auteur]

Lille économie management - UMR 9221 [LEM]
Verdebout, Thomas [Auteur]
European Center for Advanced Research in Economics and Statistics [ECARES]
Economie Quantitative, Intégration, Politiques Publiques et Econométrie [EQUIPPE]

Journal title :

Scandinavian Journal of Statistics

Pages :

249--267

Publisher :

Wiley

Publication date :

2016-11

ISSN :

0303-6898

English keyword(s) :

Estimation theory
Monte Carlo method
Big data
Kernel (Mathematics)
Stochastic approximation

HAL domain(s) :

Sciences de l'Homme et Société/Méthodes et statistiques

English abstract : [en]

Many directional data such as wind directions can be collected extremely easily so that experiments typically yield a huge number of data points that are sequentially collected. To deal with such big data, the traditional ...
Show more >Many directional data such as wind directions can be collected extremely easily so that experiments typically yield a huge number of data points that are sequentially collected. To deal with such big data, the traditional nonparametric techniques rapidly require a lot of time to be computed and therefore become useless in practice if real time or online forecasts are expected. In this paper, we propose a recursive kernel density estimator for directional data which (i) can be updated extremely easily when a new set of observations is available and (ii) keeps asymptotically the nice features of the traditional kernel density estimator. Our methodology is based on Robbins-Monro stochastic approximations ideas. We show that our estimator outperforms the traditional techniques in terms of computational time while being extremely competitive in terms of efficiency with respect to its competitors in the sequential context considered here. We obtain expressions for its asymptotic bias and variance together with an almost sure convergence rate and an asymptotic normality result. Our technique is illustrated on a wind dataset collected in Spain. A Monte-Carlo study confirms the nice properties of our recursive estimator with respect to its non-recursive counterpart. [ABSTRACT FROM AUTHOR]Show less >

Language :

Anglais

Popular science :

Non

Collections :

Lille Économie Management (LEM) - UMR 9221

Source :

Harvested from HAL

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