ISSN:
1435-926X
Keywords:
Key words: Linex loss function
;
bounded risk estimation
;
fixed-width interval estimation
;
shrinkage estimator
;
asymptotic second-order expansion
;
three-stage
;
accelerated and purely sequential stopping rules
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s001840000086
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