Simultaneous inference based on rank statistics in linear models

Abstract

A class of simultaneous tests based on the aligned rank transform (ART) statistics is proposed for linear functions of parameters in linear models. The asymptotic distributions are derived. The stability of the finite sample behaviour of the sampling distribution of the ART technique is studied by comparing the simulated upper quantiles of its sampling distribution with those of the multivariate t-distribution. Simulation also shows that the tests based on ART have excellent small sample properties and because of their robustness perform better than the methods based on the least-squares estimates.

Keywords:

• aligned rank transformation
• multiple comparisons
• simultaneous tests
• familywise error rate

AMS Subject Classifications:

• 62G10
• 62G15
• 62G20
• 62J