Rank tests in heteroscedastic multi-way HANOVA

Abstract

This article develops rank tests for the nonparametric main factor effects and interactions in multi-way high-dimensional analysis of variance when the cell distributions are completely unspecified. The design can be balanced or unbalanced with the cell sample sizes fixed or tending to infinity. An arbitrary number of factors and all types of ordinal data are allowed. This extends the use of rank methods to the Neymann–Scott and triangular array problems. The asymptotic distribution of the rank statistics is obtained by showing their asymptotic equivalence to corresponding expressions based on the asymptotic rank transform. Compared with test procedures based on the original observations, the proposed rank procedures are free of moment conditions, converge to their limiting distribution faster, and have better power when the underlying distributions are heavy tailed or skewed. These advantages are demonstrated by simulations and an application to a real data set.

Keywords:

• Neymann–Scott problem
• nonparametric hypotheses
• asymptotic distribution theory of quadratic form
• projection method
• rank tests

AMS Subject Classification :

• 62E20
• 62G30
• 62G10
• 62J12
• 62J10