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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 6, Pages 415-423
http://dx.doi.org/10.1155/S0161171200002374

Sequential risk-efficient estimation of the parameter in the uniform density

Department of Statistics, University of Kentucky, Lexington 40506, KY, USA

Received 7 October 1997; Revised 22 October 1998

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We develop a risk-efficient sequential procedure for estimating the parameter θ of the uniform density on (0,θ). We give explicit expressions for the distribution of the stopping time and derive its expectation and variance. We also tabulate the values of the expected stopping time and its standard deviation for some selected values of the parameter. Asymptotic properties such as efficiency and risk-efficiency are established.