Abstract.
The problem of estimating a linear function of k normal means with unknown variances 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, sequential stopping rules satisfying a general set of assumptions are considered. Two estimators are proposed and second-order asymptotic expansions of their risk functions are derived. It is shown that the usual estimator, namely the linear function of the sample means, is asymptotically inadmissible, being dominated by a shrinkage-type estimator. An example illustrates the use of different multistage sampling schemes and provides asymptotic expansions of the risk functions.
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Received: August 1999
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Chattopadhyay, S., Chaturvedi, A. & Sengupta, R. Sequential estimation of a linear function of normal means under asymmetric loss function. Metrika 52, 225–235 (2000). https://doi.org/10.1007/s001840000086
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DOI: https://doi.org/10.1007/s001840000086