Laplace deconvolution with dependent errors: a minimax study

Rida Benhaddou

Journal of Nonparametric Statistics, 2018, vol. 30, issue 4, 1032-1048

Abstract: We investigate the problem of estimating a function f based on observations from its noisy convolution when the noise exhibits long-range dependence (LRD). We consider both Gaussian and sub-Gaussian errors. We construct an adaptive estimator based on the kernel method, with the optimal selection of the bandwidths performed via Lepski's Method. We derive a minimax lower bound for the $ L^2 $ L2-risk when f belongs to a Sobolev ball and show that such estimator attains optimal or near-optimal rates that deteriorate as the LRD worsens. We carry out a limited simulations study which confirms our conclusions from theoretical results.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/10485252.2018.1515431 (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:30:y:2018:i:4:p:1032-1048

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

DOI: 10.1080/10485252.2018.1515431

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 ().