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September, 1977 Second Order Approximations for Sequential Point and Interval Estimation
Michael Woodroofe
Ann. Statist. 5(5): 984-995 (September, 1977). DOI: 10.1214/aos/1176343953


Several stopping times which arise from problems of sequential estimation may be written in the form $t_c = \inf\{n \geqq m: S_n < cn^\alpha L(n)\}$ where $S_n, n \geqq 1,$ are the partial sums of i.i.d. positive random variables, $\alpha > 1, L(n)$ is a convergent sequence, and $c$ is a positive parameter which is often allowed to approach zero. In this paper we find the asymptotic distribution of the excess $R_c = ct_c^\alpha - S_{t_c}$ as $c \rightarrow 0$ and use it to obtain sharp estimates for $E\{t_c\}.$ We then apply our results to obtain second order approximations to the expected sample size and risk of some sequential procedures for estimation.


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Michael Woodroofe. "Second Order Approximations for Sequential Point and Interval Estimation." Ann. Statist. 5 (5) 984 - 995, September, 1977.


Published: September, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0374.62081
MathSciNet: MR494735
Digital Object Identifier: 10.1214/aos/1176343953

Primary: 62L12
Secondary: 60F05

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 5 • September, 1977
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