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Nonparametric tests for the median from a size-biased sample

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  • Qing Kang
  • Paul Nelson

Abstract

This study explores issues related to one-sample nonparametric tests for the median of a continuous distribution when the sample is collected via size-bias of a known order. A general principle on how to construct the reference distribution of a given test statistic is presented. Following this principle, we create new bias-corrected nonparametric testing procedures. Computationally intensive, exact P-values are available for a small sample. When the sample size is large, P-values can be easily estimated by the asymptotic approximation developed here. Power functions of these tests are investigated in both small- and large-sample cases and consistency is shown to hold under fairly general conditions. The tests’ performances are then compared via asymptotic relative efficiency under four theoretical distributions.

Suggested Citation

  • Qing Kang & Paul Nelson, 2008. "Nonparametric tests for the median from a size-biased sample," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(1), pages 19-37.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:19-37
    DOI: 10.1080/10485250701830113
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