Contributions to the Theory of Dirichlet Processes

Consider a sample X₁, , Xₙ from a Dirichlet process P on an uncountable standard Borel space (X, A) where the parameter of the process is assumed to be non-atomic and -additive. Let D (n) be the number of distinct observations in the sample and denote these distinct observations by Y₁, , Y₃ (₍). Our main results are (1) D (n) / n ₀. ₒ. (X), n, and (2) given D (n), Y₁, , Y₃ (₍) are independent and identically distributed according to () / (X). Result (1) shows that (X) can be consistently estimated from the sample, and result (2) leads to a strong law for ^D (n) ₈=₁ Yᵢ/D (n).