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Low order approximations in deconvolution and regression with errors in variables

Carroll, Raymond; Hall, Peter

Description

We suggest two new methods, which are applicable to both deconvolution and regression with errors in explanatory variables, for nonparametric inference. The two approaches involve kernel or orthogonal series methods. They are based on defining a low order approximation to the problem at hand, and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently. Of course, both techniques could be employed to...[Show more]

dc.contributor.authorCarroll, Raymond
dc.contributor.authorHall, Peter
dc.date.accessioned2015-12-13T22:49:38Z
dc.date.available2015-12-13T22:49:38Z
dc.identifier.issn1369-7412
dc.identifier.urihttp://hdl.handle.net/1885/80623
dc.description.abstractWe suggest two new methods, which are applicable to both deconvolution and regression with errors in explanatory variables, for nonparametric inference. The two approaches involve kernel or orthogonal series methods. They are based on defining a low order approximation to the problem at hand, and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently. Of course, both techniques could be employed to construct consistent estimators, but in many contexts of importance (e.g. those where the errors are Gaussian) consistency is, from a practical viewpoint, an unattainable goal. We rephrase the problem in a form where an explicit, interpretable, low order approximation is available. The information that we require about the error distribution (the error-in-variables distribution, in the case of regression) is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors, e.g. through repeated measurements. In particular, we do not need to estimate a function, such as a characteristic function, which expresses detailed properties of the error distribution. This feature of our methods, coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages, means that the methods are particularly economical in computing time.
dc.publisherAiden Press
dc.sourceJournal of the Royal Statistical Society Series B
dc.subjectKeywords: Density estimation; Measurement error; Nonparametric regression; Orthogonal series; Simulation-extrapolation
dc.titleLow order approximations in deconvolution and regression with errors in variables
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume66
dc.date.issued2004
local.identifier.absfor010405 - Statistical Theory
local.identifier.ariespublicationMigratedxPub8882
local.type.statusPublished Version
local.contributor.affiliationCarroll, Raymond, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationHall, Peter, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage31
local.bibliographicCitation.lastpage46
local.identifier.doi10.1111/j.1467-9868.2004.00430.x
dc.date.updated2015-12-11T10:36:45Z
local.identifier.scopusID2-s2.0-1042267765
CollectionsANU Research Publications

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