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Saibal Chattopadhyay 《Metrika》1998,48(1):53-59
The problem of estimating a normal mean with unknown variance is considered under an asymmetric loss function such that the
associated risk is bounded from above by a known quantity. In the absence of a fixed sample size rule, a sequential stopping
rule and two sequential estimators of the mean are proposed and second-order asymptotic expansions of their risk functions
are derived. It is demonstrated that the sample mean becomes asymptotically inadmissible, being dominated by a shrinkage-type
estimator. Also a shrinkage factor is incorporated in the stopping rule and similar inadmissibility results are established.
Received September 1997 相似文献