On distribution-free tests for bivariate observations

Abstract

SUMMARY Saunders & Laud (1980) propose a multivariate goodness-of-fit test for whether the random vectors X 1 ,...,X n are a sample from a postulated distribution F . Their test can be described in terms of a univariate function of the vector observations. The inconsistency of the procedure follows by showing that there are positive nonuniform densities on the unit square which cannot be distinguished from the uniform density by Saunders & Laud's test.