, Volume 48, Issue 1, pp 53–59 | Cite as

Sequential estimation of normal mean under asymmetric loss function with a shrinkage stopping rule

  • Saibal Chattopadhyay


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.

Key words: Linex loss function bounded risk estimation shrinkage sequential stopping rule shrinkage estimators asymptotic second-order expansions 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Saibal Chattopadhyay
    • 1
  1. 1.Operations Management Group, Indian Institute of Management Calcutta, Joka, Diamond Harbour Road, PO Box 16757, Alipore Post Office, Calcutta 700027, India (e-mail:;

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