Abstract
A general, Bayesian approach to robustification via model elaboration is introduced and discussed. The approach is illustrated by considering the elaboration of standard models to incorporate the possibility of non-standard distributional shapes or of individual aberrant observations (outliers). Influence functions are then considered from a Bayesian point of view and an approach to robust time series analysis is outlined.
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References
ABRAHAM, B. and BOX, G.E.P. (1978) Linear models and spurious observations, Appl.Statist. 27, 131–8.
BERK, R.H. (1966). Limiting behaviour of posterior distributions when the model is incorrect. Ann.Math.Statist. 37, 51–8.
BIRNBAUM, A. and MIKé, V. (1970). Asympototically robust estimators of location. J.Amer.Statist.Ass. 65, 1265–82.
BOX, G.E.P. (1980). Sampling and Bayes’ inference in scientific modelling and robustness (with Discussion). J.R. Statist.Soc.A. 143, 383–430.
BOX, G.E.P. and TIAO, G.C. (1964). A Bayesian approach to the importance of assumptions applied to the comparison of variances. Biometrika, 51, 153–67.
BOX, G.E.P. and TIAO, G.C. (1968). A Bayesian approach to some outlier problems. Biometrika, 55, 119–29.
BOX, G.E.P. and TIAO, G.C. (1973). Bayesian Inference in Statistical Analysis. Reading, Mass: Addison-Wesley.
COX, D.R. and HINKLEY, D.V. (1974). Theoretical Statistics. London: Chapman Hall.
FREEMAN, P.R. (1981). On the number of outliers in data from a linear model. In Bayesian Statistics (Ed. Bernardo et al). Valencia: University Press.
GUTTMAN, I., DUTTER R. and FREEMAN, P.R. (1978). Care and handling of outliers in the general linear model to detect spurosity — a Bayesian approach. Technometrics 20, 187–93.
HAMPEL, F. (1968). Contributions to the theory of robust estimation. Ph.D. dissertation. University of California, Berkeley.
HAMPEL, F. (1974). The influence curve and its role in robust estimation. J.Amer.Statist.Ass. 69, 383–93.
HARRISON, P.J. and STEVENS, C.F. (1976). Bayesian Forecasting (with Discussion). J.R. Statist. Soc. B, 38, 205–47.
HUBER, P.J. (1964). Robust estimation of a location parameter. Ann.Math. Statist., 35, 73–101.
LINDLEY, D.V. and SMITH, A.F.M. (1972). Bayes estimates for the linear model (with Discussion). J.R.Statist.Soc. B, 34, 1–41.
MASRELIEZ, C.J. (1975). Approximate non-Gaussian filtering with linear state and observation relations. I.E.E.E. Trans. Aut. Control, AC-20, 107–110.
MASRELIEZ, C.J. and MARTIN, R.D. (1977). Robust Bayesian estimation for the linear model and robustifying the Kaiman Filter. I.E.E.E. Trans. Aut. Control, AC-22, 361–71.
NAYLOR, J. and SMITH, A.F.M. (1981). Approximate inferences for a mixture distribution. In preparation.
O’HAGAN, A. (1979). On outlier rejection phenomena in Bayes inference. J.R. Statist. Soc. B. 41, 358–67.
PETTIT, L. and SMITH, A.F.M. (1981). Bayes methods for outliers. In preparation.
RAMSAY, J.O. and NOVICK, M.R. (1980). PLU Robust Bayesian Decision Theory: Point Estimation. J. Amer. Statist. Ass. 75, 901–07.
RELLES, D.A. and ROGERS, W.H. (1977). Statisticians are fairly robust estimators of location. J. Amer. Statist. Ass. 72, 107–11.
SMITH, A.F.M. and SPIEGELHALTER, D.J. (1981). Bayes factors and choice criteria for linear models. J.R. Statist. Soc. B, 42, 213–20.
SPIEGELHALTER, D.J. (1977). A test for normality against symmetric alternatives. Biometrika 64, 415–18.
SPIEGELHALTER, D.J. (1978). Adaptive Inference using a Finite Mixture Model. Ph.D. dissertation. University College London.
SPIEGELHALTER, D.J. (1980). An omnibus test for normality for small samples. Biometrika, 67, 493–96.
SPIEGELHALTER, D.J. (1981). Sampling properties of a finite mixture model. Unpublished manuscript. University of Nottingham.
STIGLER, S.M. (1977). Do robust estimators work with real data? Ann. Statist. 5, 1055–98.
TUKEY, J.W. (1960). A survey of sampling from contaminated distributions. In Contributions to Probability and Statistics: Essays in Honour of Harold Hotelling. Stanford University Press.
UTHOFF, V.A. (1970). An optimum test property of two well-known statistics. J. Amer. Statist. Ass. 65, 1597–1600.
UTHOFF, V.A. (1973). The most powerful scale and location invariant test of the normal against the double exponential. Ann. Statist. 1, 170–74.
WEST, M. (1981). Robust sequential approximate Bayesian estimation. J.R. Statist. Soc. B, 43. 157–66.
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Smith, A.F.M. (1983). Bayesian Approaches to Outliers and Robustness. In: Florens, J.P., Mouchart, M., Raoult, J.P., Simar, L., Smith, A.F.M. (eds) Specifying Statistical Models. Lecture Notes in Statistics, vol 16. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5503-1_2
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DOI: https://doi.org/10.1007/978-1-4612-5503-1_2
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