On optimal estimation of the mode in nonparametric deconvolution problems

Barbara Wieczorek

Journal of Nonparametric Statistics, 2010, vol. 22, issue 1, 65-80

Abstract: This work deals with the problem of estimating the mode in nonparametric deconvolution models. First, given n i.i.d. observations from Y=X+ϵ, we consider estimating the mode θ of a density function of some random variable X. Second, we consider the errors-in-variables regression model, where we are interested in the mode of m(x)=E(Z|X=x), where n i.i.d. observations from (Y, Z) with Y=X+ϵ are given. In both cases, we assume the distribution of ϵ to be ordinary smooth. The mode estimator ˆθn is defined via maximising over a curve estimator of the kernel type. In both deconvolution models, we obtain rates for the quadratic risk of ˆθn, depending on the smoothness of the underlying curve and the degree of ill-posedness of the deconvolution problem. Further, we show that these rates are optimal, considering one-dimensional subproblems in the class of functions studied.

Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/10485250903121626 (text/html)
Access to full text is restricted to subscribers.

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:taf:gnstxx:v:22:y:2010:i:1:p:65-80

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/GNST20

DOI: 10.1080/10485250903121626

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().