## SIGNIFICANCE TEST IN BIVARIATE CANONICAL CORRELATION ANALYSIS

### Nuffield College, Oxford University

### 15 September 1997

Summary

Canonical correlation analysis provides an example of a significance test which is not even asymptotically similar. For most values of the nuisance parameter a standard asymptotic distribution approximation applies, whereas for some particular parameter values, which may not be of practical interest, a different approximation applies. Therefore the asymptotic distribution and also Bartlett corrections to not have a uniform effect. It is suggested to use an asymptotic approximation which depends continuously on the nuisance parameter.