Robust response transformations based on optimal prediction

Details

Serval ID
serval:BIB_76320FC570CB
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Robust response transformations based on optimal prediction
Journal
Journal of the American Statistical Association
Author(s)
Marazzi Alfio, Villar Ana J., Yohai Victor J.
ISSN
0162-1459
Publication state
Published
Issued date
2009
Peer-reviewed
Oui
Volume
104
Number
485
Pages
360-370
Language
english
Notes
Supplemental material: http://pubs.amstat.org/doi/suppl/10.1198/jasa.2009.0109
Abstract
Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.
Web of science
Create date
03/02/2010 15:47
Last modification date
20/08/2019 14:33
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