Communications for Statistical Applications and Methods

  • 제31권4호
  • /
  • Pages.427-440
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  • 2024
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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On the Bayes risk of a sequential design for estimating a mean difference

  • Sangbeak Ye (Methods Center, University of Tubingen) ;
  • Kamel Rekab (Department of Mathematics and Statistics, University of Missouri Kansas City)
  • 투고 : 2024.01.01
  • 심사 : 2024.03.18
  • 발행 : 2024.07.31
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초록

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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참고문헌

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