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March, 1982 Sequential Estimation Through Estimating Equations in the Nuisance Parameter Case
Pedro E. Ferreira
Ann. Statist. 10(1): 167-173 (March, 1982). DOI: 10.1214/aos/1176345698


Let $(X_1, X_2, \cdots)$ be a sequence of random variables and let the p.d.f. of $\mathbf{X}_n = (X_1, \cdots, X_n)$ be $p(\mathbf{x}_n, \theta)$, where $\theta = (\theta_1, \theta_2)$. An estimating equation rule for $\theta_1$ is a sequence of functions $g(x_1, \theta_1), g(x_1, x_2, \theta_1), \cdots$. If the random sample size $N = n$, we estimate $\theta_1$ through the estimating equation $g(\mathbf{X}_n, \theta_1) = 0$. In this paper, optimum estimation rules are obtained and, in particular, sufficient conditions for the optimality of the maximum conditional likelihood estimation rule are given. In addition, Bhapkar's concept of information in an estimating equation is used to discuss stopping criteria.


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Pedro E. Ferreira. "Sequential Estimation Through Estimating Equations in the Nuisance Parameter Case." Ann. Statist. 10 (1) 167 - 173, March, 1982.


Published: March, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0485.62081
MathSciNet: MR642727
Digital Object Identifier: 10.1214/aos/1176345698

Primary: 62F10
Secondary: 62L12

Keywords: Estimating equation , nuisance parameter , stopping rule

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 1 • March, 1982
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