Sequential estimation of a linear function of normal means under asymmetric loss function |
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| Authors: | Saibal Chattopadhyay Ajit Chaturvedi Raghu Nandan Sengupta |
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| Affiliation: | (1) Department of Mathematics and Statistics, 810 Oldfather Hall, PO Box 880323, Lincoln NE 68588-0323 USA, E-mail: chattopa@hotmail.com, schattop@math.unl.edu, US;(2) Department of Statistics, Allahabad University, India, IN;(3) Indian Institute of Management Calcutta Joka, PO Box 16757, Alipore PO, Calcutta 700027 INDIA, E-mail: raghu_n_sengupta@hotmail.com, IN |
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| 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. Received: August 1999 |
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| Keywords: | : Linex loss function bounded risk estimation fixed-width interval estimation shrinkage estimator asymptotic second-order expansion three-stage accelerated and purely sequential stopping rules |
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