An Asymptotic Second-Order Lower Bound for the Bayes Risk of a Sequential Procedure

Rekab, Kamel; Tahir, Mohamed

doi:10.1081/sqa-200027055

Cited by 4 publications

(1 citation statement)

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“…In the literature, while two-stage and three-stage designs have received extensive analysis leading typically in linear estimation to first and second order asymptotic optimality respectively, cf. Ghosh et al (1997); Rekab and Tahir (2004) and the references therein, there does not appear, to our knowledge, to be work in which second order asymptotic optimality is rigorously analyzed in the case of non linear estimation. The focus in this work is on second order asymptotic optimality of 2-and 3-stage designs for estimating a product of several Bernoulli proportions under the constraint of a total and fixed sample size T large enough.…”

Section: Introductionmentioning

confidence: 92%

Nearly second order three-stage design for estimating a product of several Bernoulli proportions

Benkamra

Terbeche

Tlemcani

2015

Journal of Statistical Planning and Inference

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Section: Introductionmentioning

confidence: 92%

Nearly second order three-stage design for estimating a product of several Bernoulli proportions

Benkamra

Terbeche

Tlemcani

2015

Journal of Statistical Planning and Inference

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Second Order Optimality of Sequential Designs with Application in Software Reliability Estimation

Rekab¹

2015

BBIJ

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We propose three efficient sequential designs in the software reliability estimation. The fully sequential design the multistage sequential design and the accelerated sequential design. These designs make allocation decisions dynamically throughout the testing process. We then refine these estimated reliabilities in an iterative manner as we sample. Monte Carlo simulation seems to indicate that these sequential designs are second order optimal.

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On the Bayes risk of a sequential design for estimating a mean difference

Ye,

Rekab

2024

Communications for Statistical Applications and Methods

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The problem addressed is that of sequentially estimating the difference between the means of two populations with respect to the squared error loss, where each population distribution is a member of the one-parameter exponential family. A Bayesian approach is adopted in which the population means are estimated by the posterior means at each stage of the sampling process and the prior distributions are not specified but have twice continuously differentiable density functions. The main result determines an asymptotic second-order lower bound, as t → ∞, for the Bayes risk of a sequential procedure that takes M observations from the first population and t − M from the second population, where M is determined according to a sequential design, and t denotes the total number of observations sampled from both populations.

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An Asymptotic Second-Order Lower Bound for the Bayes Risk of a Sequential Procedure

Cited by 4 publications

References 10 publications

Nearly second order three-stage design for estimating a product of several Bernoulli proportions

Nearly second order three-stage design for estimating a product of several Bernoulli proportions

Second Order Optimality of Sequential Designs with Application in Software Reliability Estimation

On the Bayes risk of a sequential design for estimating a mean difference

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