I have a very large number of observations. Observations arrive sequentially. Each observation is an $n$-dimensional vector (with $n \ge 100$), is independent from the others and is drawn from the same unknown distribution. Is there an optimal policy to estimate the unknown distribution, given some space bounds on the number of observations that can be stored? I would leave the estimation criteria open-ended, (in terms of expected or minimax error, asymptotic consistency, aysmptotic efficiency etc.).
If you have no reason to suspect more than one mode in your data, then a multivariate normal distribution is not a bad first go. You just calculate the mean vector, and covariance matrix, and there's your PDF.
However this is a very rough answer, and it seems to me that with 100 observations, you will probably have multi-modal data. Normal just looks like one big smooth multi-dimensional mountain. You data would probably look more like a multi-dimensional mountain range (with lots of local humps).