Minimax Robustness of Bayesian Forecasting under Functional Distortions of Probability Densities
DOI:
https://doi.org/10.17713/ajs.v31i2&3.480Abstract
The problems of robustness in Bayesian forecasting are considered under distortions of the hypothetical probability densities. The expressions for the guaranteed upper risk functional are obtained and the robust prediction statistics under certain types of distortions are constructed.References
V.M. Alexeev. Optimal control. Science, Moscow, 1979. In Russian.
J. Berger. Statistical Decision Theory and Bayesian Analysis. Springer, New York, 1985.
J. Berger, B. Betro, and E. Moreno et al., editors. Bayesian Robustness, volume 29 of IMS Lecture Notes — Monograph Series. IMS, Hayward, 1996.
A.A. Borovkov. Mathematical Statistics. Science, Novosibirsk, 1997. In Russian.
R. Dutter. On robust estimation of variograms in geostatistics. In Robust Statistics, Data Analysis, and Computer Intensive Methods, volume 109 of Lecture Notes in Statistics, pages 153–172. Springer, New York, 1996.
V. Galinskij and A. Kharin. On minimax robustness of Bayesian statistical prediction. In Grigelionis B., editor, Probability Theory and Mathematical Statistics, pages 259–266, Vilnius/Utrecht/Tokio, 1998. VSP/TEV.
F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W. Stahel. Robust Statistics. The Approach Based on Influence Functions. Wiley & Sons, New York, 1986.
P.J. Huber. Robust Statistics. Wiley, New York, 1981.
M. Meczarski. Problemy Odpornosci w Bayesowskiej Analizie Statystycznej. Szkola Glowna Handlowa, Warszawa, 1998. In Polish.
J. Pilz. Bayesian spatial prediction using the matern class of covariance functions. In International Data Analysis Conference 2000: Abstracts, Innsbruck, 2000.
H. Rieder. Robust Asymptotic Statistics. Springer–Verlag, New York, 1994.
R. Viertl. Statistical Methods for Non-Precise Data. CRC Press, Boca Raton, 1996.
M. West and J. Harrison. Bayesian Forecasting and Dynamic Models. Springer–Verlag, New York, 1989.
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