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Nonexistence of informative unbiased estimators in singular problems. (English) Zbl 0783.62026
The authors show the nonexistence of informative unbiased estimators in all singular problems. They consider both the case of fixed sample size and asymptotical, including most problems with optimal rate of convergence slower than $n\sp{-1/2}$. They also discuss situations in regular problems where such nonexistence can occur.

MSC:
62G05Nonparametric estimation
62F10Point estimation
62F12Asymptotic properties of parametric estimators
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