caa a22 4500 475793358 CHVBK 20180406123716.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1007/s001840000086 doi (NATIONALLICENCE)springer-10.1007/s001840000086 Sequential estimation of a linear function of normal means under asymmetric loss function [Elektronische Daten] [Saibal Chattopadhyay, Ajit Chaturvedi, Raghu Nandan Sengupta] 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. Springer-Verlag Berlin Heidelberg, 2000 Key words: Linex loss function nationallicence bounded risk estimation nationallicence fixed-width interval estimation nationallicence shrinkage estimator nationallicence asymptotic second-order expansion nationallicence three-stage nationallicence accelerated and purely sequential stopping rules nationallicence Chattopadhyay Saibal 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 aut Chaturvedi Ajit Department of Statistics, Allahabad University, India, IN aut Sengupta Raghu Nandan Indian Institute of Management Calcutta Joka, PO Box 16757, Alipore PO, Calcutta 700027 INDIA, E-mail: raghu_n_sengupta@hotmail.com, IN aut https://doi.org/10.1007/s001840000086 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001840000086 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chattopadhyay Saibal 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 aut NATIONALLICENCE 700 1- Chaturvedi Ajit Department of Statistics, Allahabad University, India, IN aut NATIONALLICENCE 700 1- Sengupta Raghu Nandan Indian Institute of Management Calcutta Joka, PO Box 16757, Alipore PO, Calcutta 700027 INDIA, E-mail: raghu_n_sengupta@hotmail.com, IN aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer