Abstract
The Bayesian analysis of outliers using a non-informative prior for the parameters is non-trivial because models with different numbers of outliers have different dimensions. A quasi-Bayesian approach based on the Akaike's predictive likelihood is proposed for the analysis of regression outliers. It overcomes the dimensionality problem in Bayesian outlier analysis in which the likelihood of the outlier model is compensated by a correction factor adjusted for the number of outliers. The stack loss data set is analysed with satisfactory results.
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References
Abraham, B. and Box, G.E.P. (1978). Linear models and spurious observations.Appl. Statist.,27, 131–138.
Aitchison, J. (1975). Goodness of prediction fit.Biometrika,62, 547–554.
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle.2nd Int. Symp. on Information Theory (ed.) B.N. Petrov and F. Caski), Akademiai Kiado, Bdapest, 267–281.
Akaike, H. (1980). On the use of the predictive likelihood of a Gaussian model.Ann. Inst. Statist. Math., A32, 311–324.
Andrews, D.F. (1974). A robust method for multiple linear regression.Technometrics,16, 523–531.
Atkinson, A.C. (1978). Posterior probabilities for choosing a regression model.Biometrika,65, 39–48.
Bacon-Shone, J. (1986). MAXLIK—A library for maximum likelihood estimation on micros.Research Report, University of Hong Kong.
Barnett, V. and Lewis, T. (1984).Outliers in Statistical Data. Second ed. New York: John Wiley.
Brownlee, K.A. (1965).Statistical Theory and Methodology in Science and Engineering. Second edition, John Wiley.
Daniel, C. and Wood, F.S. (1980).Fitting Equations to Data. Second edition. New York: John Wiley.
Freeman, P.R. (1981). On the number of outliers in data from a linear model.Bayesian Statistics (Bernardo, J.M., et al. eds.), 349–365. Valencia: University Press.
Fung, W.K. (1987). Analysis of outliers using Akaike's predictive likelihood approach, paper presented at the17th European Meeting of Statisticians.
Fung W.K. (1989). Quasi-Bayesian estimation of Stigler's data sets.Computat. Statist. & Data Analysis,7, 237–243.
Guttman, I., Dutter, R. and Freeman, P.R. (1978). Care and handling of univariate outliers in the general linear model to detect spuriosity— a Bayesian approach.Technometrics,20, 187–193.
Hawkins, D.M. (1980).Identification of Outliers. Chapman and Hall, London.
Hawkins, D.M., Bardu, D. and Kass, G.V. (1984). Location of several outliers in multiple-regression data using elemental sets.Technometrics, 197–208.
Kitagawa, G. (1984). Bayesian analysis of outliers via Akaike's predictive likelihood of a model.Commun. Statist.—Simula. Computa.,13, 107–126.
Pettit, L.I. and Smith, A.F.M. (1985). Outliers and influential observations in linear models (with discussion).Bayesian Statistics 2, (Bernardo, J.M., et. al. eds.), 473–494. Valencia: University Press.
Prescott, P. (1975). An approximate test for outliers in linear models.Technometrics,17, 129–132.
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Fung, W.K. A quasi-Bayesian analysis of regression outliers using Akaike's predictive likelihood. Statistical Papers 34, 133–141 (1993). https://doi.org/10.1007/BF02925535
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DOI: https://doi.org/10.1007/BF02925535