Moderate Deviations and Large Deviations for Kernel Density Estimators

Fuqing Gao ()
Additional contact information
Fuqing Gao: Wuhan University

Journal of Theoretical Probability, 2003, vol. 16, issue 2, 401-418

Abstract: Abstract Let f n be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random variables taking values in ℝ d . It is proved that if the kernel function is an integrable function with bounded variation, and the common density function f of the random variables is continuous and f(x) → 0 as |x| → ∞, then the moderate deviation principle and large deviation principle for $$\{ \sup _{x \in \mathbb{R}^d } |f_n (x) - E(f_n (x))|,n \geqslant 1\} $$ hold.

Keywords: kernel density estimator; moderate deviations; large deviations (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1023/A:1023574711733 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:jotpro:v:16:y:2003:i:2:d:10.1023_a:1023574711733

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1023574711733

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().