  We provide a complete asymptotic distribution theory for clustered data with
a large number of independent groups, generalizing the classic laws of large
numbers, uniform laws, central limit theory, and clustered covariance matrix
estimation. Our theory allows for clustered observations with heterogeneous and
unbounded cluster sizes. Our conditions cleanly nest the classical results for
i.n.i.d. observations, in the sense that our conditions specialize to the
classical conditions under independent sampling. We use this theory to develop
a full asymptotic distribution theory for estimation based on linear
least-squares, 2SLS, nonlinear MLE, and nonlinear GMM.
