Abstract
The analysis of regression data is often improved by using a transformation of the response rather than the original response itself. However, finding a suitable transformation can be strongly affected by the influence of a few individual observations. Outliers can have an enormous impact on the fitting of statistical models and can be hard to detect due to masking and swamping. These difficulties are enhanced in the case of models for dependent observations, since any anomalies are with respect to the specific autocorrelation structure of the model. In this paper we develop a forward search approach which is able to robustly estimate the Box-Cox transformation parameter under a first-order spatial autoregression model.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
ATKINSON, A.C. and RIANI, M. (2000): Robust Diagnostic Regression Analysis. Springer, New York.
ATKINSON, A.C., RIANI, M. and CERIOLI, A. (2004): Exploring Multivariate Data with the Forward Search. Springer, New York.
BOX, G.E.P. and COX, D.R. (1964): An Analysis of Transformations (with discussion). Journal of the Royal Statistical Society B, 26, 211–246.
CERIOLI, A. and RIANI, M. (2002): Robust Methods for the Analysis of Spatially Autocorrelated Data. Statistical Methods and Applications-Journal of the Italian Statistical Society, 11, 335–358.
CRESSIE, N.A.C. (1993): Statistics for Spatial Data. Wiley, New York.
GRIFFITH, D.A. and LAYNE, L.J. (1999): A Casebook for Spatial Statistical Data Analysis. Oxford University Press, New York.
PACE, R.K., BARRY, R., SLAWSON, V.C. Jr. and SIRMANS, C.F. (2004): Simultaneous Spatial and Functional Form Transformations. In: L. Anselin, R.J.G.M. Florax and S.J. Rey (Eds.): Advances in Spatial Econometrics. Springer, New York.
RIPLEY, B.D. (1988): Statistical Inference for Spatial Processes. Cambridge University Press, Cambridge.
ROUSSEEUW, P.J. and van ZOMEREN, B.C. (1990): Unmasking Multivariate Outliers and Leverage Points. Journal of the American Statistical Association, 85, 633–639.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Berlin · Heidelberg
About this paper
Cite this paper
Cerioli, A., Riani, M. (2006). Robust Transformations and Outlier Detection with Autocorrelated Data. In: Spiliopoulou, M., Kruse, R., Borgelt, C., Nürnberger, A., Gaul, W. (eds) From Data and Information Analysis to Knowledge Engineering. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31314-1_31
Download citation
DOI: https://doi.org/10.1007/3-540-31314-1_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31313-7
Online ISBN: 978-3-540-31314-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)