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Biometrika 2002 89(4):939-946; doi:10.1093/biomet/89.4.939
© 2002 by Biometrika Trust
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Miscellanea

Forward search added-variable t-tests and the effect of masked outliers on model selection

Anthony C.Atkinson1 and Marco Riani2

1 Department of Statistics, London School of Economics, London WC2A 2AE, U.Ka.c.atkinson{at}lse.ac.uk 2 Dipartimento di Economia, Università di Parma, 43100 Parma, Italy mriani{at}unipr.it

Monitoring the t-tests for individual regression coefficients in ‘forward’ search fails to identify the importance of observations to the significance of the individual regressors. This failure is due to the ordering of the data by the search. We introduce an added-variable test which has the desired properties since the projection leading to residuals destroys the effect of the ordering.An example illustrates the effect of several masked outliers on model selection. Comments are given on the related test for response transformations.

Key Words: Box-Cox transformation; Projection; Score statistic; t-distribution; Transformation to normality; Very robust methods

Received February 2002. Revised April 2002


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