International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 6, Pages 415-423
doi: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 Z. Govindarajulu. 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.