PCA-kernel estimation

Biau Gérard and Mas André
Additional contact information
Mas André: Institut de Math´ematiques et de Modelisation de Montpellier, Equipe de Probabilites et Statistique, Montpellier Cedex 5, Frankreich

Statistics & Risk Modeling, 2012, vol. 29, issue 1, 19-46

Abstract: Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample X1,...,Xn onto the first D eigenvectors of the Principal Component Analysis (PCA) associated with the empirical projector ^ ΠD. Classical nonparametric inference methods such as kernel density estimation or kernel regression analysis are then performed in the (usually small) D-dimensional 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 (^ΠDX1,...,^ΠDXn) 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.

Keywords: principal component analysis; dimension reduction; nonparametric kernel estimation; density estimation; regression estimation (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1524/strm.2012.1084 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:29:y:2012:i:1:p:19-46:n:3

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/strm/html

DOI: 10.1524/strm.2012.1084

Access Statistics for this article

Statistics & Risk Modeling is currently edited by Robert Stelzer

More articles in Statistics & Risk Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().