In order to form a maximum likelihood estimate (MLE), you must have a likelihood function. If \(y_1, \ldots, y_n \sim f(y_i|\theta)\), where \(f(y_i|\theta)\) is a density function indexed by \(\theta\), then the likelihood function is given by \(L(\theta|y_1,\ldots,y_n) = \prod_{i=1}^n f(y_i|\theta)\). Of course, without an explicit density function, we can't go much farther than this in computing an MLE.

In general, no more than one observation is required in order to compute a MLE. However, the MLE may not be unique. This problem is called *unidentifiability*. That is, when there are few observations, the MLE may be a poor estimate of \(\theta\).