INVESTIGATION OF DECISION THEORY WITH CORRELATED RANDOM VARIABLES.

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)

Document Details

Document Type
Technical Report
Publication Date
Jul 03, 1968
Accession Number
AD0673376

Entities

People

  • Robert Bohrer

Organizations

  • RTI International

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Consistency
  • Contracts
  • Convergence
  • Covariance
  • Decision Theory
  • Estimators
  • Markov Processes
  • Mathematics
  • Observation
  • Random Variables
  • Sequences
  • Spectra
  • Stationary
  • Test And Evaluation

Fields of Study

  • Mathematics

Readers

  • Software Engineering
  • Statistical inference.