Statistics Papers
Document Type
Journal Article
Date of this Version
7-1978
Publication Source
The Annals of Statistics
Volume
6
Issue
4
Start Page
932
Last Page
934
DOI
10.1214/aos/1176344269
Abstract
In Wegman's paper [5] on nonparametric density estimation, he states that it would be interesting to show that there is no density estimator which has mean integrated square rate better than O(n-1). The object of this note is to prove such a result, making no arbitrary assumptions about the specific form of the estimator. This proof is given in Section 2. Our method applies to some other measures of error, as we point out in Section 3.
Keywords
Nonparametric, density estimation, mean integrated square error, Cramér-Rao inequality
Recommended Citation
Boyd, D. W., & Steele, J. M. (1978). Lower Bounds for Nonparametric Density Estimation Rates. The Annals of Statistics, 6 (4), 932-934. http://dx.doi.org/10.1214/aos/1176344269
Date Posted: 27 November 2017
This document has been peer reviewed.
Comments
At the time of publication, author J. Michael Steele was affiliated with University of British Columbia. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.