The required sample size for estimating a multivariate joint histogram is something that I expect to depend on multiple factors such as the distributional properties of the data-generating process (e.g. multivariate Gaussian vs Pareto), choice of bin endpoints, number of bins, and the number of variables. Therefore I don't expect a single number for the appropriate sample size, but perhaps a collection of functions or other relations.
Are there relations/bounds/functions for working out (possibly conservative) sample size requirements for estimating multivariate histograms?
