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Asymptotic risk robustness of statistical decision rules in the presence of dependent samples. (English) Zbl 0728.62007

Asymptotic statistics, 4th Prague Symp., Prague/Czech. 1988, 329-335 (1989).
[For the entire collection see Zbl 0692.00015.]
The supposed model of the training sample, used for multivariate statistical decision rule construction, is frequently distorted for real data. That is why the problem of robustness estimation for decision rules is very topical. In the author’s paper, Asymptotic statistics, Proc. 3rd Prague Symp. 1983, Asymptotic Stat. 2, 309-316 (1984; Zbl 0571.62049), this problem is solved for the case when training sample distortions are conditioned by a “contamination”. Here by the risk asymptotic expansion method we investigate the new topical situation when the traditional hypothesis about the independence of observations is broken.

MSC:

62C10 Bayesian problems; characterization of Bayes procedures
62F12 Asymptotic properties of parametric estimators
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62F35 Robustness and adaptive procedures (parametric inference)