
Accession Number : AD0732307
Title : Contributions to the Theory of Dirichlet Processes,
Corporate Author : FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
Personal Author(s) : Korwar,Ramesh M. ; Hollander,Myles
Report Date : OCT 1971
Pagination or Media Count : 28
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, ..., i1, 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)
Descriptors : (*STATISTICAL PROCESSES, MEASURE THEORY), PROBABILITY DENSITY FUNCTIONS, STOCHASTIC PROCESSES, DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, SET THEORY, THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE