Article Dans Une Revue Statistics & Risk Modeling with Applications in Finance and Insurance Année : 2012

PCA-Kernel Estimation

Résumé

Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample $\bX_1, \hdots, \bX_n$ onto the first $D$ eigenvectors of the Principal Component Analysis (PCA) associated with the empirical projector $\hat \Pi_D$. Classical nonparametric inference methods such as kernel density estimation or kernel regression analysis are then performed in the (usually small) $D$-di\-men\-sio\-nal space. However, the mathematical analysis of this data-driven dimension reduction scheme raises technical problems, due to the fact that the random variables of the projected sample $( \hat \Pi_D\bX_1,\hdots, \hat \Pi_D\bX_n )$ are no more independent. As a reference for further studies, we offer in this paper several results showing the asymptotic equivalencies between important kernel-related quantities based on the empirical projector and its theoretical counterpart. As an illustration, we provide an in-depth analysis of the nonparametric kernel regression case

Fichier principal
Vignette du fichier
KPCAv3.pdf (240.92 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence
Loading...

Dates et versions

hal-00467013 , version 1 (25-03-2010)

Licence

Identifiants

Citer

Gérard Biau, André Mas. PCA-Kernel Estimation. Statistics & Risk Modeling with Applications in Finance and Insurance, 2012, 29 (1), pp.19-46. ⟨10.1524/strm.2012.1084⟩. ⟨hal-00467013⟩
616 Consultations
699 Téléchargements

Altmetric

Partager

  • More