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If you could assume multivariate normality (which you said you could not) you could do a Hotelling T2 test of equality of mean vectors to see if you could claim differences between distributions or not. However although you can't do that you can still theoretically compare the distributions to see if they differ much. Divide the 30 dimensional space into rectangular grids. Use these as 30 dimensional bins. Count the number of vectors falling into each bin and apply a chi square test to see if the distributions look the same. The problem with this suggestion is that it requires judiciously selecting the bins in order to cover the data points in an appropriate way. Also the curse of dimensionality makes it difficult to identify differences between the multivariate distributions without having a very large number of point in each group. I think suggestions that gui11aume gave are sensible. I don't think the others are. Since comparing the distributions is not feasible in 30 dimensions with a typical sample some form of valid comparison of the mean vectors would seem to me to be appropriate/.

If you could assume multivariate normality (which you said you could not) you could do a Hotelling T2 test of equality of mean vectors to see if you could claim differences between distributions or not. However although you can't do that you can still theoretically compare the distributions to see if they differ much. Divide the 30 dimensional space into rectangular grids. Use these as 30 dimensional bins. Count the number of vectors falling into each bin and apply a chi square test to see if the distributions look the same. The problem with this suggestion is that it requires judiciously selecting the bins in order to cover the data points in an appropriate way. Also the curse of dimensionality makes it difficult to identify differences between the multivariate distributions without having a very large number of point in each group. I think suggestions that gui11aume gave are sensible. I don't think the others are. Since comparing the distributions is not feasible in 30 dimensions with a typical sample some form of valid comparison of the mean vectors would seem to me to be appropriate.

If you could assume multivariate normality (which you said you could not) you could do a Hotelling T2 test of equality of mean vectors to see if you could claim differences between distributions or not. However although you can't do that you can still compare the distributions to see if they differ much. Divide the 30 dimensional space into rectangular grids. Use these as 30 dimensional bins. Count the number of vectors falling into each bin and apply a chi square test to see if the distributions look the same.

If you could assume multivariate normality (which you said you could not) you could do a Hotelling T2 test of equality of mean vectors to see if you could claim differences between distributions or not. However although you can't do that you can still theoretically compare the distributions to see if they differ much. Divide the 30 dimensional space into rectangular grids. Use these as 30 dimensional bins. Count the number of vectors falling into each bin and apply a chi square test to see if the distributions look the same. The problem with this suggestion is that it requires judiciously selecting the bins in order to cover the data points in an appropriate way. Also the curse of dimensionality makes it difficult to identify differences between the multivariate distributions without having a very large number of point in each group. I think suggestions that gui11aume gave are sensible. I don't think the others are. Since comparing the distributions is not feasible in 30 dimensions with a typical sample some form of valid comparison of the mean vectors would seem to me to be appropriate/.

If you could assume multivariate normality (which you said you could not) you could do a Hotelling T2 test of equality of mean vectors to see if you could claim differences between distributions or not. However although you can't do that you can still compare the distributions to see if they differ much. Divide the 30 dimensional space into rectangular grids. Use these as 30 dimensional bins. Count the number of vectors falling itno each bin and apply a chi square test to see if the distributions look the same.

If you could assume multivariate normality (which you said you could not) you could do a Hotelling T2 test of equality of mean vectors to see if you could claim differences between distributions or not. However although you can't do that you can still compare the distributions to see if they differ much. Divide the 30 dimensional space into rectangular grids. Use these as 30 dimensional bins. Count the number of vectors falling into each bin and apply a chi square test to see if the distributions look the same.