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, ..., 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)

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