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Linking the estimation and ranking and selection problems through sequential procedures: The normal case

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  • Chaturvedi, Ajit
  • Gupta, Rahul

Abstract

Taking into consideration the relationship among the 'optimal' fixed sample size solutions of estimation (point, as well as, interval) and ranking and selection problems related to normal populations, a class of sequential procedures is developed. The confidence interval and ranking and selection problems are linked with the bounded risk point estimation problems under some suitable loss functions. Exploiting the common functional form of the risks associated with these problems, second-order approximations are obtained for the 'regret'. It is illustrated that the results obtained under this general set-up provide second-order approximations to estimation and ranking and selection problems and, as such, no separate dealing is required. As an additional contribution, a much simple technique of obtaining the asymptotic distribution of stopping time is provided.

Suggested Citation

  • Chaturvedi, Ajit & Gupta, Rahul, 1994. "Linking the estimation and ranking and selection problems through sequential procedures: The normal case," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 273-285, July.
    • Handle: RePEc:eee:stapro:v:20:y:1994:i:4:p:273-285
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