I found out that my research data do not meet the requirements of canonical and discriminant analysis (the number of observations is very small while the number of independant variables is big and also there is no variable normality despite data transformations). I need to analyse the influance of a group of many independant variables on many dependant variables. I also plan to detect the independant variables which determine given classification (discriminant analysis would work well for this if meeting the assumptions). I have problems with finding a non-parametric method for this or overcoming the assumption problem.
I would much appreciate any suggestions.