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March, 1993 Sequential Estimation Results for a Two-Parameter Exponential Family of Distributions
Arup Bose, Benzion Boukai
Ann. Statist. 21(1): 484-502 (March, 1993). DOI: 10.1214/aos/1176349038


We consider the problem of sequentially estimating one parameter in a class of two-parameter exponential family of distributions. We assume a weighted squared error loss with a fixed cost of estimation error. The stopping rule, based on the maximum likelihood estimate of the nuisance parameter, is shown to be independent of the terminal estimate. The asymptotic normality of the stopping variable is established and approximations to its mean and to the regret associated with it are also provided. The general results are exemplified by the normal, gamma and the inverse Gaussian densities.


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Arup Bose. Benzion Boukai. "Sequential Estimation Results for a Two-Parameter Exponential Family of Distributions." Ann. Statist. 21 (1) 484 - 502, March, 1993.


Published: March, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0770.62066
MathSciNet: MR1212189
Digital Object Identifier: 10.1214/aos/1176349038

Primary: 62L12
Secondary: 62E99

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 1 • March, 1993
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