Discrete-transform approach to deconvolution problems
-
Altmetric Citations
Description
If Fourier series are used as the basis for inference in deconvolution problems, the effects of the errors factorise out in a way that is easily exploited empirically. This property is the consequence of elementary addition formulae for sine and cosine functions, and is not readily available when one is using methods based on other orthogonal series or on continuous Fourier transforms. It allows relatively simple estimators to be constructed, founded on the addition of finite series rather than...[Show more]
dc.contributor.author | Hall, Peter | |
---|---|---|
dc.contributor.author | Qiu, Peihua | |
dc.date.accessioned | 2015-12-13T22:45:26Z | |
dc.identifier.issn | 0006-3444 | |
dc.identifier.uri | http://hdl.handle.net/1885/79785 | |
dc.description.abstract | If Fourier series are used as the basis for inference in deconvolution problems, the effects of the errors factorise out in a way that is easily exploited empirically. This property is the consequence of elementary addition formulae for sine and cosine functions, and is not readily available when one is using methods based on other orthogonal series or on continuous Fourier transforms. It allows relatively simple estimators to be constructed, founded on the addition of finite series rather than on integration. The performance of these methods can be particularly effective when edge effects are involved, since cosineseries estimators are quite resistant to boundary problems. In this context we point to the advantages of trigonometric-series methods for density deconvolution; they have better mean squared error performance when edge effects are involved, they are particularly easy to code, and they admit a simple approach to empirical choice of smoothing parameter, in which a version of thresholding, familiar in wavelet-based inference, is used in place of conventional smoothing. Applications to other deconvolution problems are briefly discussed. | |
dc.publisher | Biometrika Trust | |
dc.source | Biometrika | |
dc.subject | Keywords: Cosine series; Deconvolution; Fourier series; Ill-posed problem; Measurement error; Nonparametric density estimation; Nonparametric regression; Orthogonal series; Regularisation; Smoothing; Thresholding; Trigonometric series; Wavelet | |
dc.title | Discrete-transform approach to deconvolution problems | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.description.refereed | Yes | |
local.identifier.citationvolume | 92 | |
dc.date.issued | 2005 | |
local.identifier.absfor | 010405 - Statistical Theory | |
local.identifier.ariespublication | MigratedxPub8163 | |
local.type.status | Published Version | |
local.contributor.affiliation | Hall, Peter, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Qiu, Peihua, University of Minnesota | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.issue | 1 | |
local.bibliographicCitation.startpage | 135 | |
local.bibliographicCitation.lastpage | 148 | |
local.identifier.doi | 10.1093/biomet/92.1.135 | |
dc.date.updated | 2015-12-11T10:22:05Z | |
local.identifier.scopusID | 2-s2.0-15844379328 | |
Collections | ANU Research Publications |
Download
File | Description | Size | Format | Image |
---|---|---|---|---|
01_Hall_Discrete-transform_approach_to_2005.pdf | 523.78 kB | Adobe PDF | Request a copy |
Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.
Updated: 17 November 2022/ Responsible Officer: University Librarian/ Page Contact: Library Systems & Web Coordinator