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On second order admissibility in simultaneous estimation. (English) Zbl 0686.62017
Mathematical statistics theory and applications, Proc. World Congr. Bernoulli Soc., Tashkent/USSR 1986, Vol. 2, 225-235 (1987).
[For the entire collection see Zbl 0671.00013.]
The differential inequality plays an important part in verification of admissibility of estimators. The author considers the case of simultaneous estimation. A necessary and sufficient condition is given for the existence of an estimator admitting a risk expansion up to the second order. It is also shown that an estimator is second order admissible if and only if there does not exist a nontrivial positive solution to the differential inequality. Further, a necessary and sufficient condition is given for second order admissibility of the maximum likelihood estimator in some family of distributions.
Reviewer: M.Akahira
MSC:
62F12 Asymptotic properties of parametric estimators
62C15 Admissibility in statistical decision theory