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Optimal equivariant estimator with respect to convex loss function. (English) Zbl 0914.62044

Summary: Consider a family of probability distributions which is invariant under a group of transformations. We define an optimality criterion with respect to an arbitrary convex loss function and we prove a characterization theorem for an equivariant estimator to be optimal. We illustrate this theorem under some conditions on convex loss functions.

MSC:

62H12 Estimation in multivariate analysis
62F10 Point estimation
62F99 Parametric inference
62A01 Foundations and philosophical topics in statistics
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