Robust response transformations based on optimal prediction

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...

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Detalles Bibliográficos
Autor principal:	Villar, Ana Julia
Publicado:	2009
Materias:	Box-cox transformations Conditional expectation Heteroscedasticity Robust estimation Smearing estimate
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v104_n485_p360_Marazzi http://hdl.handle.net/20.500.12110/paper_01621459_v104_n485_p360_Marazzi
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_01621459_v104_n485_p360_Marazzi
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spelling	paper:paper_01621459_v104_n485_p360_Marazzi2023-06-08T15:13:37Z Robust response transformations based on optimal prediction Villar, Ana Julia Box-cox transformations Conditional expectation Heteroscedasticity Robust estimation Smearing estimate 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. © 2009 American Statistical Association. Fil:Villar, A.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v104_n485_p360_Marazzi http://hdl.handle.net/20.500.12110/paper_01621459_v104_n485_p360_Marazzi
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Box-cox transformations Conditional expectation Heteroscedasticity Robust estimation Smearing estimate
spellingShingle	Box-cox transformations Conditional expectation Heteroscedasticity Robust estimation Smearing estimate Villar, Ana Julia Robust response transformations based on optimal prediction
topic_facet	Box-cox transformations Conditional expectation Heteroscedasticity Robust estimation Smearing estimate
description	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. © 2009 American Statistical Association.
author	Villar, Ana Julia
author_facet	Villar, Ana Julia
author_sort	Villar, Ana Julia
title	Robust response transformations based on optimal prediction
title_short	Robust response transformations based on optimal prediction
title_full	Robust response transformations based on optimal prediction
title_fullStr	Robust response transformations based on optimal prediction
title_full_unstemmed	Robust response transformations based on optimal prediction
title_sort	robust response transformations based on optimal prediction
publishDate	2009
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v104_n485_p360_Marazzi http://hdl.handle.net/20.500.12110/paper_01621459_v104_n485_p360_Marazzi
work_keys_str_mv	AT villaranajulia robustresponsetransformationsbasedonoptimalprediction
_version_	1768544546454503424

Robust response transformations based on optimal prediction

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