Accession Number : AD0673376

Title :   INVESTIGATION OF DECISION THEORY WITH CORRELATED RANDOM VARIABLES.

Descriptive Note : Final rept. 15 Jun 67-14 Jun 68,

Corporate Author : RESEARCH TRIANGLE INST DURHAM N C STATISTICS RESEARCH DIV

Personal Author(s) : Bohrer,Robert

Report Date : 03 JUL 1968

Pagination or Media Count : 5

Abstract : Empirical Bayes decision theory with correlated random variables were studied by R. Bohrer. A general stationary time series setting for some Empirical Bayes problems is defined. Asymptotically optimum (Bayes) solutions are derived when the spectrum of the observation process and the observation-parameter process cross-spectrum are known. For the case when only observation-parameter covariances are known, a least-squares sequence of estimators is proposed and sufficient conditions for its consistency established. Sequential design risk evaluation were studied by R. Bohrer. Work begun under Contract AF 49(638)1544 is extended and refined. Risks are evaluated exactly in cases for which only non-design formulae were known previously. The renewal density matrix of a semi-Markov process were studied by J. J. Hunter. The problem of multivariate renewal theory is defined for semi-Markov processes. Necessary, sufficient, and necessary and sufficient conditions for convergence of a renewal density matrix are derived. (Author)

Descriptors :   (*DECISION THEORY, STATISTICAL PROCESSES), CORRELATION TECHNIQUES, RANDOM VARIABLES, TIME SERIES ANALYSIS, PROBABILITY, OPTIMIZATION, LEAST SQUARES METHOD

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE