Universal weighted kernel-type estimators for some class of regression models

Igor S. Borisov (), Yuliana Yu. Linke () and Pavel S. Ruzankin ()
Additional contact information
Igor S. Borisov: Sobolev Institute of Mathematics
Yuliana Yu. Linke: Sobolev Institute of Mathematics
Pavel S. Ruzankin: Sobolev Institute of Mathematics

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 2, No 2, 166 pages

Abstract: Abstract For a wide class of nonparametric regression models with random design, we suggest consistent weighted least square estimators, asymptotic properties of which do not depend on correlation of the design points. In contrast to the predecessors’ results, the design is not required to be fixed or to consist of independent or weakly dependent random variables under the classical stationarity or ergodicity conditions; the only requirement being that the maximal spacing statistic of the design tends to zero almost surely (a.s.). Explicit upper bounds are obtained for the rate of uniform convergence in probability of these estimators to an unknown estimated random function which is assumed to lie in a Hölder space a.s. A Wiener process is considered as an example of such a random regression function. In the case of i.i.d. design points, we compare our estimators with the Nadaraya–Watson ones.

Keywords: Nonparametric regression; Uniform consistency; Kernel-type estimator; 62G08 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s00184-020-00768-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:metrik:v:84:y:2021:i:2:d:10.1007_s00184-020-00768-0

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-020-00768-0

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().