A multivariate signed-rank test for the one-sample location problem

Dawn Peters, Ronald H. Randles

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


An affine-invariant signed-rank test is proposed for the one-sample multivariate location problem. The test suggested is a modification of Randles’s multivariate sign test based on interdirections, which extends Blumen’s bivariate procedure to the multidimensional setting. Comparisons are made between the proposed statistic and several competitors via Pitman asymptotic relative efficiencies and Monte Carlo results. The signed-rank statistic appears to be robust. It performs better than its competitors when the distribution is light-tailed, and virtually as well as Hotelling’s T2 under multivariate normality. For heavy-tailed distributions the signed-rank statistic performs better than Hotelling’s T2 but not as well as Randles’s statistic.

Original languageEnglish (US)
Pages (from-to)552-557
Number of pages6
JournalJournal of the American Statistical Association
Issue number410
StatePublished - Jun 1990
Externally publishedYes


  • Affine-invariant
  • Interdirections
  • One sample
  • Sign test

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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