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On the coverage probabilities of parametric confidence bands for continuous distribution and quantile functions constructed via confidence regions for a location-scale parameter

Author

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  • Fabian Mies

    (RWTH Aachen University)

  • Stefan Bedbur

    (RWTH Aachen University)

Abstract

In parametric statistics, confidence bands for continuous distribution (quantile) functions may be constructed by unifying the graphs of all distribution (quantile) functions corresponding to parameters lying in some confidence region. It is then desirable that the coverage probabilities of both, band and region, coincide, e.g., to prevent from wide and less informative bands or to transfer the property of unbiasedness; this is ensured if the confidence region is exhaustive. Properties and representations of exhaustive confidence regions are presented. In location-scale families, the property of some confidence region to be exhaustive depends on the boundedness of the supports of the distributions in the family. For unbounded, one-sided bounded and bounded supports, characterizations of exhaustive confidence regions are derived. The results are useful to decide whether the trapezoidal confidence regions based on the standard pivotal quantities are exhaustive and may serve to construct exhaustive confidence regions in (log-)location-scale models.

Suggested Citation

  • Fabian Mies & Stefan Bedbur, 2017. "On the coverage probabilities of parametric confidence bands for continuous distribution and quantile functions constructed via confidence regions for a location-scale parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 925-944, August.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:4:d:10.1007_s10463-016-0570-0
    DOI: 10.1007/s10463-016-0570-0
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    References listed on IDEAS

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    1. R. Srinivasan & R. Wharton, 1976. "Further results on simultaneous confidence intervals for the normal distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 28(1), pages 25-33, December.
    2. Hong, Yili & Escobar, Luis A. & Meeker, William Q., 2010. "Coverage probabilities of simultaneous confidence bands and regions for log-location-scale distributions," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 733-738, April.
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