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Minimum volume confidence sets for parameters of normal distributions

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  • Jin Zhang

    (Yunnan University)

Abstract

Under a proper restriction, we establish the minimum volume confidence set (interval and region) for parameter of any normal distribution. Compared with classical methods, the proposed confidence region is proved to be the best with minimum area, for whatever confidence level, sample size and sample data.

Suggested Citation

  • Jin Zhang, 2017. "Minimum volume confidence sets for parameters of normal distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(3), pages 309-320, July.
    • Handle: RePEc:spr:alstar:v:101:y:2017:i:3:d:10.1007_s10182-017-0290-7
    DOI: 10.1007/s10182-017-0290-7
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    References listed on IDEAS

    as
    1. Bradley Efron, 2006. "Minimum volume confidence regions for a multivariate normal mean vector," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 655-670, September.
    2. Liu, W. & Hayter, A.J., 2007. "Minimum Area Confidence Set Optimality for Confidence Bands in Simple Linear Regression," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 181-190, March.
    3. Nagao, Hisao & Srivastava, M. S., 2002. "Fixed Width Confidence Region for the Mean of a Multivariate Normal Distribution," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 259-273, May.
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    Cited by:

    1. Bedbur, S. & Kamps, U. & Lennartz, J.M., 2019. "On a smallest confidence region for a location–scale parameter in progressively type-II censored lifetime experiments," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.

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