Contributions to the Theory of Dirichlet Processes

摘要: Abstract : The authors derive some basic properties of a sample X(1),...,X(n) from Dirichlet process. Let r(i) = 0 if X(i) X(k) for k 1, ..., i-1, and 1 otherwise. They first establish the distribution summation i=1 to n r(i), number distinct observations in sample, certain conditional unconditional joint distributions X(i)'s r(i)'s. These results are used prove weak law large numbers Z sub (the (r(i) X(i))/ r(i). is then applied obtain consistency Bayes estimator index transition measure mixture processes. (Author)