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On the convergence rate of sequential fixed-width confidence intervals for normal parameters

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  • Isogai, Eiichi
  • Futschik, Andreas

Abstract

We consider the convergence rate of sequential fixed-width confidence intervals for [theta]=a[mu]+b[sigma] under a normal model with [mu] and [sigma]2 both unknown. We use the fully sequential procedure proposed by [Takada, Y., 1997. Fixed-width confidence intervals for a function of normal parameters. Sequential Anal. 16, 107-117] to construct sequential confidence intervals for [theta] and investigate the convergence rate of the coverage probability as the width of the confidence interval approaches zero. We also derive a second-order asymptotic expansion of the average sample size.

Suggested Citation

  • Isogai, Eiichi & Futschik, Andreas, 2008. "On the convergence rate of sequential fixed-width confidence intervals for normal parameters," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1826-1834, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1826-1834
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    References listed on IDEAS

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    1. Keiichi Hirose & Eiichi Isogai & Chikara Uno, 1997. "The Convergence Rate of Fixed-Width Sequential Confidence Intervals for a Parameter of an Exponential Distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 199-209, June.
    2. Nitis Mukhopadhyay & Sujay Datta, 1996. "On sequential fixed-width confidence intervals for the mean and second-order expansions of the associated coverage probabilities," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 497-507, September.
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