Estimation non paramétrique des quantile

Abstract

L’estimationnonparam´etriqueenstatistiqueestl’unedesm´ethodescourantesetvalides quim`enent`adesr´esultatssatisfaisants. Lebutprincipaldenotrem´emoireestd’appliquerlam´ethodenonparam´etriquepour estimerlafonctionquantileenutilisantlam´ethodedunoyauquiestcaract´eris´eepar lechoixdunoyauetduparam`etredelissageappel´eaussifenˆetredelissage.Lechoix duparam`etredelissageestcrucialpourlapr´ecisionlocaleainsiquepourlapr´ecisionglobaledel’estimateur.Enfindecompte,nousavonsenrichinotretravailavecunepartied’applicationnum´erique,ou`nousavonsfaitunecomparaisonentrel’estimateurempirique etl’estimateur`anoyaudelafonctionquantile.

Nonparametricestimationinstatisticsisoneofthecommonandvalidmethodsthatleadtosatisfyingresults. The main goal of our dissertation is to apply the non-parametric method to estimate thequantile function using the kernel method which is characterized by the choice of thekernel and the smoothing parameter, also called smoothing window.The choice of thesmoothing parameter is crucial for the local precision as well as for the global precisionof the estimator. At last, we enriched our work with a numerical application part, wherewe made a comparison between the empirical estimator and the kernel estimator of thequantilefunction.