Edgeworth approximations for rank sum test statistics

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Abstract

Hettmansperger (1984) quotes a result showing that the distribution function of the Wilcoxon signed rank statistic is approximated by the usual Edgeworth series using the first four cumulants, to 0(n-1). In light of standard Edgeworth series results for random variables confined to a lattice, this result is counterintuitive. One expects correction terms to be necessary because of the lattice nature of the Wilcoxon statistic. This paper explains this apparent paradox, provides an alternative proof relying on basic Edgeworth series results, and provides a sharper result. Interesting features in this problem highlighting limitations of expansions for random variables on a lattice are discussed.

Original languageEnglish (US)
Pages (from-to)169-171
Number of pages3
JournalStatistics and Probability Letters
Volume24
Issue number2
DOIs
StatePublished - Aug 1 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Edgeworth series
  • Lattice distributions
  • Wilcoxon statistic

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