Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal experiments under asymmetric loss. (English) Zbl 1268.62012

Bhattacharya, Debasis; Basu, A. K.

Rojo, Javier (ed.), Optimality. The second Erich L. Lehmann symposium. Selected papers based on the presentations at the symposium, Houston, TX, USA, May 19–22, 2004. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-66-9/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 49, 312-321 (2006).

Summary: Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal families of distributions are investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the bound is obtained.
For the entire collection see [Zbl 1113.62002].

MSC:

62C20	Minimax procedures in statistical decision theory
62B15	Theory of statistical experiments
62F12	Asymptotic properties of parametric estimators
62E20	Asymptotic distribution theory in statistics

Keywords:

locally asymptotically mixture of normal experiments; local asymptotic minimax risk bound; asymmetric loss functions