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Improving Hall’s Accelerated Sequential Procedure: Generalized Multistage Fixed-Width Confidence Intervals for a Normal Mean

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Abstract

We have developed an innovative generalized multistage fixed-width confidence interval (FWCI) estimation procedure for an unknown normal mean when the variance also remains unknown, which can be viewed as a mixture of sequential sampling and batch sampling procedures. Requiring the same expected sample size as Hall’s accelerated sequential sampling procedure, it enables the number of sampling operations to be further reduced by a predetermined factor. Extensive sets of simulations are provided to highlight the remarkable performance of the new multistage FWCI estimation procedure, and real data illustrations are included to demonstrate the practical applicability.

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References

  • Anscombe FJ (1952) Large-sample theory of sequential estimation. In: Proceedings of Cambridge philosophical society, 48, pp 600–607. Cambridge University Press

  • Anscombe F J (1953) Sequential Estimation. J Roy Statist Soc Series B 15:1–29

    MathSciNet  MATH  Google Scholar 

  • Dantzig G B (1940) On the non-existence of tests of Student’s hypothesis having power functions independent of σ. Ann Math Statist 11:186–192

    Article  MathSciNet  Google Scholar 

  • Chow Y S, Robbins H (1965) On the asymptotic theory of fixed-width sequential confidence intervals for the mean. Ann Math Statist 36:457–462

    Article  MathSciNet  Google Scholar 

  • Hall P (1981) Asymptotic theory of triple sampling for estimation of a mean. Ann Statist 9:1229–1238

    MathSciNet  MATH  Google Scholar 

  • Hall P (1983) Sequential estimation saving sampling operations. J Roy Statist Soc Series B 45:219–223

    MathSciNet  MATH  Google Scholar 

  • Hu J, Mukhopadhyay N (2019) Second-order asymptotics in a class of purely sequential minimum risk point estimation (MRPE) methodologies. Japanese. J Statist Data Sci 2:81–104

    Article  Google Scholar 

  • Hu J, Zhuang Y (2019) A generalized sequential sampling design with fewer sampling operations. Submitted

  • Lai T L, Siegmund D (1977) A nonlinear renewal theory with applications to sequential analysis I. Ann Statist 5:946–954

    MathSciNet  MATH  Google Scholar 

  • Lai T L, Siegmund D (1979) A nonlinear renewal theory with applications to sequential analysis II. Ann Statist 7:60–76

    MathSciNet  MATH  Google Scholar 

  • Liu W (1997) A k-stage sequential sampling procedure for estimation of normal mean. J Statist Plan Inf 65:109–127

    Article  MathSciNet  Google Scholar 

  • Mukhopadhyay N (1990) Some properties of a three-stage procedure with applications in sequential analysis. Sankhya, Series A 52:218–231

    MathSciNet  MATH  Google Scholar 

  • Mukhopadhyay N (1996) An alternative formulation of accelerated sequential procedures with applications to parametric and nonparametric estimation. Seq Anal 15:253–269

    Article  MathSciNet  Google Scholar 

  • Mukhopadhyay N, Bapat S R (2018) Purely sequential bounded-risk point estimation of the negative binomial mean under various loss functions: one-sample problem. Ann Inst Statist Math 70:1049–1075

    Article  MathSciNet  Google Scholar 

  • Mukhopadhyay N, de Silva BM (2009) Sequential methods and their applications. CRC, Boca Ratton

    MATH  Google Scholar 

  • Mukhopadhyay N, Solanky TKS (1994) Multistage selection and ranking procedures: Second order asymptotics, vol 2. CRC Press

  • Mukhopadhyay N, Son M S, Ko Y C (2004) A new two-stage sampling design for estimating the maximum average time to flower. J Agri Biol Envir Statist 9:479–499

    Article  Google Scholar 

  • Simons G (1968) On the cost of not knowing the variance when making a fixed-width confidence interval for the mean. Ann Math Statist 39:1946–1952

    Article  MathSciNet  Google Scholar 

  • Stein C (1945) A two sample test for a linear hypothesis whose power is independent of the variance. Ann Math Statist 16:243–258

    Article  MathSciNet  Google Scholar 

  • Woodroofe M (1977) Second order approximations for sequential point and interval estimation. Ann Statist 5:984–995

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author thanks anonymous reviewers for their valuable comments that helped preparing this revised manuscript.

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  1. Department of Mathematics and Statistics, Oakland University, Rochester, MI, 48309, USA

    Jun Hu

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  1. Jun Hu
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Correspondence to Jun Hu.

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Hu, J. Improving Hall’s Accelerated Sequential Procedure: Generalized Multistage Fixed-Width Confidence Intervals for a Normal Mean. Methodol Comput Appl Probab 23, 823–835 (2021). https://doi.org/10.1007/s11009-020-09786-x

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  • DOI: https://doi.org/10.1007/s11009-020-09786-x

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