Recursive estimators of integrated squared density derivatives

Abdelkader Mokkadem and Mariane Pelletier

Statistics & Probability Letters, 2020, vol. 157, issue C

Abstract: Hall and Marron (1987) introduced kernel estimators of integrals of various squared derivatives of a probability density. The aim of this paper is the study of recursive versions of their estimators. Rates of convergence in mean squared error (MSE) are calculated. Similarly to the estimators of Hall and Marron (1987), the recursive estimators may achieve the parametric rate n−1; the striking fact is that their MSE are then equivalent to those of their nonrecursive versions, whereas the recursive nonparametric estimators are known for usually having larger MSE than their nonrecursive version. We also provide recursive estimators of the optimal bandwidth in the framework of density estimation.

Keywords: Recursive estimation; Kernel estimators of integrals; Stochastic algorithm; Mean squared error; Rate of convergence (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016771521930255X
Full text for ScienceDirect subscribers only

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:eee:stapro:v:157:y:2020:i:c:s016771521930255x

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2019.108609

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().