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A journey in single steps: robust one-step M-estimation in linear regression.

Welsh, Alan; Ronchetti, E.

Description

We present a unified treatment of different types of one-step M-estimation in regression models which incorporates the Newton-Raphson, method of scoring and iteratively reweighted least squares forms of one-step estimator. We use higher order expansions to distinguish between the different forms of estimator and the effects of different initial estimators. We show that the Newton-Raphson form has better properties than the method of scoring form which, in turn, has better properties than the...[Show more]

dc.contributor.authorWelsh, Alan
dc.contributor.authorRonchetti, E.
dc.date.accessioned2015-12-13T22:23:18Z
dc.identifier.issn0378-3758
dc.identifier.urihttp://hdl.handle.net/1885/72715
dc.description.abstractWe present a unified treatment of different types of one-step M-estimation in regression models which incorporates the Newton-Raphson, method of scoring and iteratively reweighted least squares forms of one-step estimator. We use higher order expansions to distinguish between the different forms of estimator and the effects of different initial estimators. We show that the Newton-Raphson form has better properties than the method of scoring form which, in turn, has better properties than the iteratively reweighted least squares form. We also show that the best choice of initial estimator is a smooth, robust estimator which converges at the rate n-1/2. These results have important consequences for the common data-analytic strategy of using a least squares analysis on "clean" data obtained by deleting observations with extreme residuals from an initial least squares fit. It is shown that the resulting estimator is an iteratively reweighted least squares one-step estimator with least squares as the initial estimator, giving it the worst performance of the one-step estimators we consider: inferences resulting from this strategy are neither valid nor robust.
dc.publisherElsevier
dc.sourceJournal of Statistical Planning and Inference
dc.subjectBreakdown point
dc.subjectDiagnostics
dc.subjectInfluence function
dc.subjectIteratively reweighted least squares estimator
dc.subjectM-estimator
dc.subjectMethod of scoring estimator
dc.subjectNewton-Raphson estimator
dc.subjectOutliers
dc.subjectRejection method
dc.subjectS-estimator
dc.titleA journey in single steps: robust one-step M-estimation in linear regression.
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume103
dc.date.issued2002
local.identifier.absfor010405 - Statistical Theory
local.identifier.ariespublicationMigratedxPub3393
local.type.statusPublished Version
local.contributor.affiliationWelsh, Alan, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationRonchetti, E, University of Geneva
local.description.embargo2037-12-31
local.bibliographicCitation.startpage287
local.bibliographicCitation.lastpage310
local.identifier.doi10.1016/S0378-3758(01)00228-2
dc.date.updated2015-12-11T08:04:39Z
local.identifier.scopusID2-s2.0-0037089981
CollectionsANU Research Publications

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