Optimal variance estimation based on lagged second-order difference in nonparametric regression

WenWu Wang (), Lu Lin and Li Yu
Additional contact information
WenWu Wang: Shandong University
Lu Lin: Shandong University
Li Yu: China Re Asset Management Company LTD

Computational Statistics, 2017, vol. 32, issue 3, No 11, 1047-1063

Abstract: Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only $$n^{1/2}$$ n 1 / 2 -consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample.

Keywords: Least squares; Nonparametric variance estimation; Optimal differenced estimator (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s00180-016-0666-2 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:compst:v:32:y:2017:i:3:d:10.1007_s00180-016-0666-2

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-016-0666-2

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().