A note on the integrated squared error of a kernel density estimator in non-smooth cases

Bert van Es

Statistics & Probability Letters, 1997, vol. 35, issue 3, 241-250

Abstract: Let X1, ... , Xn be a random sample from a distribution on the real line with an unknown density f. We discuss the performance of the kernel density estimator of the density f. The properties of kernel estimators in cases where the density f to be estimated is sufficiently smooth are well known. Instead we focus on estimation problems where f is non-smooth, i.e. f is allowed to have a finite number of jumps or kinks. Thus the robustness properties of the kernel estimator against unfulfilled smoothness assumptions are illustrated. After a review of properties of the mean integrated squared error we present a central limit theorem for the integrated squared error. This theorem extends results of Bickel, Rosenblatt and Hall. Finally, the distance between the bandwidth minimizing the integrated squared error and the bandwidth which minimizes the mean integrated squared error is discussed.

Keywords: Density; estimation; Kernel; estimators; Integrated; squared; error; Central; limit; theorem (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(97)00019-9
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:35:y:1997:i:3:p:241-250

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

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 ().