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We obtain the empirical strong law of large numbers, empiricalGlivenko-Cantelli theorem, central limit theorem, functional central limittheorem for various nonparametric Bayesian priors which include the Dirichletprocess with general stick-breaking weights, the Poisson-Dirichlet process, thenormalized inverse Gaussian process, the normalized generalized gamma process,and the generalized Dirichlet process. For the Dirichlet process with generalstick-breaking weights, we introduce two general conditions such that thecentral limit theorem and functional central limit theorem hold. Except in thecase of the generalized Dirichlet process, since the finite dimensionaldistributions of these processes are either hard to obtain or are complicatedto use even they are available, we use the method of moments to obtain theconvergence results. For the generalized Dirichlet process we use its finitedimensional marginal distributions to obtain the asymptotics although thecomputations are highly technical.

Functional central limit theorems for stick-breaking priors