question about how important the joint normality assumption is:
I have a data set where I feel good about marginal distributions of y_1 y_2 y_3 being gaussian, can model them separately just fine, but not sure about them being jointly normal (similar to teardrop shape on multivariate analysis - Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? - Cross Validated ) due to some heteroskedacity or something,
can choosing a good kernel on cross-covariance deal with something like this or would I need some other strategy in general for a combined model?