Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data

Salim Bouzebda and Boutheina Nemouchi

Journal of Nonparametric Statistics, 2020, vol. 32, issue 2, 452-509

Abstract: W. Stute [(1991), Annals of Probability, 19, 812–825] introduced a class of so-called conditional U-statistics, which may be viewed as a generalisation of the Nadaraya–Watson estimates of a regression function. Stute proved their strong pointwise consistency to \[ m(\mathbf{ t}):=\mathbb{E}[\varphi(Y_{1},\ldots,Y_{m})|(X_{1},\ldots,X_{m})=\mathbf{t}],\quad \mbox{for } \mathbf{t}\in \mathbb{R}^{dm}. \] m(t):=E[ϕ(Y1,…,Ym)|(X1,…,Xm)=t],for t∈Rdm. We apply the methods developed in Dony and Mason [(2008), Bernoulli, 14(4), 1108–1133] to establish uniformity in $\mathbf {t} $t and in bandwidth consistency (i.e. $h_{n} $hn, $h_{n}\in [a_{n},b_{n}] $hn∈[an,bn] where $0

Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://hdl.handle.net/10.1080/10485252.2020.1759597 (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:taf:gnstxx:v:32:y:2020:i:2:p:452-509

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/GNST20

DOI: 10.1080/10485252.2020.1759597

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().