Contributions to the Theory of Dirichlet Processes,
Abstract
The authors derive some basic properties of a sample X(1),...,X(n) from a Dirichlet process. Let r(i) = 0 if X(i) = X(k) for some k = 1, ..., i-1, and 1 otherwise. They authors first establish the distribution of the summation from i=1 to n of r(i), the number of distinct observations in the sample, and certain conditional and unconditional joint distributions of the X(i)'s and r(i)'s. These results are used to prove a weak law of large numbers for Z sub n = (the summation from i=1 to n of (r(i) X(i))/ the summation from i=1 to n of r(i). The weak law is then applied to obtain the consistency of a Bayes estimator of the index of the transition measure of a mixture of Dirichlet processes. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1971
- Accession Number
- AD0732307
Entities
People
- Myles Hollander
- Ramesh M. Korwar
Organizations
- Florida State University