Confidence Coefficients of Interpolated Nonparametric Sign Intervals for Medians Under No or Weak Shape Assumptions

  • Olivier Guilbaud
Part of the Statistics for Industry and Technology book series (SIT)


Non-parametric “sign” intervals for a parent median based on order statistics have the important property of being generally valid. With small sample sizes, the available confidence coefficients (CCs) are sparse, however, and it is natural to try to interpolate between adjacent sign intervals to attain intermediate levels. This chapter provides the CC associated with weighted means of adjacent sign intervals over some interesting classes of parent distributions, including: (a) all distributions, (b) all symmetric distributions, and (c) all symmetric and unimodal distributions. The behavior of these CCs as functions of the weight is simple but intuitively quite surprising, with certain discontinuities and intervals of constancy. Some unexpected domination relations among weighted means of adjacent sign intervals follow from these results. The resulting nondominated intervals constitute a considerable extension of the sign intervals, with substantially more confidence-coefficient levels; and they are valid under no or weak shape assumptions about the parent distribution.

Keywords and phases

Confidence interval general distribution interpolation median nonparametric order statistic symmetric distribution unimodal distribution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Beran, R., and Hall, P. (1993). Interpolated nonparametric prediction intervals and confidence intervals, Journal of the Royal Statistical Society, Series B, 55, 643–652.zbMATHMathSciNetGoogle Scholar
  2. 2.
    David, H. A., and Nagaraja, H. N. (2003). Order Statistics, Third edition, John Wiley_& Sons, Hoboken, NJ.zbMATHGoogle Scholar
  3. 3.
    Dharmadhikari, S. and Joag-dev, K. (1988). Unimodality, Convexity, and Applications, Academic Press, San Diego.zbMATHGoogle Scholar
  4. 4.
    Guilbaud, O. (1979). Interval estimation of the median of a general distribution, Scandinavian Journal of Statistics, 6, 29–36.MathSciNetGoogle Scholar
  5. 5.
    Hettmansperger, T. P., and Sheather, S. J. (1986). Confidence intervals based on interpolated order statistics, Statistics_& Probability Letters, 4, 75–79.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hutson, A. D. (1999). Calculating nonparametric confidence intervals for quantiles using fractional order statistics, Journal of Applied Statistics, 26, 343–353.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Noether, G. E. (1973). Some simple distribution-free confidence intervals for the center of a symmetric distribution, Journal of the American Statistical Association, 68, 716–719.zbMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • Olivier Guilbaud
    • 1
  1. 1.AstraZenecaSödertäljeSweden

Personalised recommendations