Asymptotic Robustness of Bayesian Decision Rules in Statistical Decision Theory
We consider the statistical classification problems when conditional probability distributions of observations are given with distortions. Robust decision rules are derived for Tukey’s model with contaminating distributions and for the model with additive distortions of observations. The guaranteed risk values for robust and Bayesian decision rules are found and compared by the method of asymptotic expansions. The results are illustrated for the case of Gaussian observations.
KeywordsAsymptotic Expansion Decision Rule Conditional Probability Distribution Statistical Decision Theory Unknown Density
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- Kharin, Yu.S. About the statistical classification efficiency by using minimum contrast estimators. Probab. Theory and Appl., XXVI (1981) 866–867.Google Scholar
- Rey, W. J. J. Robust statistical methods. Lect. not in Math., 690 (1978).Google Scholar
- Tukey, J. W. A survey of sampling from contaminated distributions. In: Contrib. to Prob. and Statist., Stanford, 1960.Google Scholar