Summary
A new method for dealing with possibly contaminated data, when there exists prior information about the contamination procedure, is proposed and studied in order to obtain robust estimators. A class of Bayesian robust estimators is then established and its properties studied. Applications of the proposed method are given.
Similar content being viewed by others
References
Barnett, V. and Lewis, T. (1984).Outliers in Statistical Data. Wiley.
Berger, J. O. and Mortera, J. (1990). Bayesian analysis with limited communication.Uppsala Abstracts, 2nd World Congress of the Bernoulli Society for Mathematical Statistics and Probability and 53rd Annual Meeting of the Institute of Mathematical Statistics. (G.P.H., Styan, ed.).
Diaconis, P. and Freedman, D. (1986). On the consistency of Bayes estimates.Ann. Statist. 14, 1–26.
García Pérez, A. (1992). Bayesian robustness of the empirical distribution.Tech. Rep. 2 Facultad de Ciencias, U.N.E.D. Madrid
Kharin, Y.S. (1983). Robustness of decision rules in the presence of errors of classification of the training sample.Automation and Remote Control 44, 1470–1479.
O’Hagan, A. (1979). On outlier rejection phenomena in Bayes inference.J. Roy. Statist. Soc. B 41, 358–367.
O’Hagan, A. (1988). Modelling with heavy tails.Bayesian Statistics 3 (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.). Oxford: University Press
Pettit, L. I. and Smith, A. F. M. (1985). Outliers and influential observations in linear models.Bayesian Statistics 2 (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.), Amsterdam: North-Holland
Ritov, Y. (1985). Robust Bayes decision procedures: gross error in the data distribution.Ann. Statist. 13, 626–637.
West, M. (1984). Outlier models and prior distributions in Bayesian linear regression.J. Roy. Statist. Soc. B 46, 431–439.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
García-Pérez, A. Bayesian robustness of the empirical distribution. Test 3, 183–194 (1994). https://doi.org/10.1007/BF02562680
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02562680