Robust Box-Cox transformations based on minimum residual autocorrelation

Authors:
Alfio Marazzi;Victor J. Yohai
Affiliations:
Institute for Social and Preventive Medicine, University of Lausanne, Bugnon 17, CH 1005 Lausanne, Switzerland;Departamento de Matematica, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon 1, 1428 Buenos Aires, Argentina
Venue:
Computational Statistics & Data Analysis
Year:
2006

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Abstract

Response transformations are a popular approach to adapt data to a linear regression model. The regression coefficients, as well as the parameter defining the transformation, are often estimated by maximum likelihood assuming homoscedastic normal errors. Unfortunately, consistency to the true parameters holds only if the assumptions of normality and homoscedasticity are satisfied. In addition, these estimates are nonrobust in the presence of outliers. New estimates are proposed, which are robust and consistent even if the assumptions of normality and homoscedasticity do not hold. These estimates are based on the minimization of a robust measure of residual autocorrelation.