Abstract.
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.
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Received September 1997
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Chattopadhyay, S. Sequential estimation of normal mean under asymmetric loss function with a shrinkage stopping rule. Metrika 48, 53–59 (1998). https://doi.org/10.1007/s001840050005
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DOI: https://doi.org/10.1007/s001840050005