Regression operator estimation by delta-sequences method for functional data and its applications

Idir Ouassou () and Mustapha Rachdi ()

AStA Advances in Statistical Analysis, 2012, vol. 96, issue 4, 465 pages

Abstract: In this paper, we introduce a somewhat more general class of nonparametric estimators (delta-sequences estimators) for estimating an unknown regression operator from noisy data. The regressor is assumed to take values in an infinite-dimensional separable Banach space, when the response variable is a scalar. Under some general conditions, we establish the uniform almost-complete convergence with the rates of these estimators. Moreover, we give some particular cases of our results, which can also be considered as novel in the finite-dimensional setting. Moreover, after giving some examples of the impact of our results, we show how to use them in some statistical applications (prediction procedure and curve discrimination). Copyright Springer-Verlag 2012

Keywords: Nonparametric regression operator estimation; Functional data; Strong consistency; Method of delta-sequences; Measure theory on a Banach space; Small ball probabilities (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10182-011-0175-0 (text/html)
Access to full text is restricted to subscribers.

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:spr:alstar:v:96:y:2012:i:4:p:451-465

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10182/PS2

DOI: 10.1007/s10182-011-0175-0

Access Statistics for this article

AStA Advances in Statistical Analysis is currently edited by Göran Kauermann and Yarema Okhrin

More articles in AStA Advances in Statistical Analysis from Springer, German Statistical Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().