Bent Nielsen (1998) 'Conditional test for rank in bivariate canonical correlation analysis' ABSTRACT: The likelihood ratio test for the hypothesis that the smallest of two canonical correlations is zero is non-similar. This means that the distribution of the test statistic depends on a nuisance parameter: the value of the largest canonical correlation. If this parameter were known it would be possible to construct a test with a desired size. However, in applications the nuisance parameter is usually estimated. It is therefore of interest to evaluate the distributional properties of such a test, conditional on the estimator. This distribution is found. Although, it depends on the nuisance parameter, the dependency seems to be negligible for practical purposes.