I am trying to classify a set of $p$ predictors into 5 classes. But my sample size $n$ is rather small, so I fear I won't get a very robust estimate.
Now an idea would be to subset my data for each of the 5 response classes, and simulate more data in each class. I would e.g. assume a multivariate normal distribution for the predictors, and then (I think some people call this a parametric bootstrap) estimate $\mu$ and $\Sigma$ from the multivariate normal, and with those parameters then simulate 10000 new observations in this class. I would do this for every class and then have 50000 additional observations.
Given that I simulate the data from only the knowledge I have from my small sample, is there anything I can gain with this procedure? Robustness yes, but I will certainly not get more information, right?
Does this approach make sense at all? Is there maybe already a better way to solve this problem?