Open Access
March, 1979 On Dynamic Programming and Statistical Decision Theory
Manfred Schal
Ann. Statist. 7(2): 432-445 (March, 1979). DOI: 10.1214/aos/1176344625

Abstract

The main aim of the present work is to establish connections between the theory of dynamic programming and the statistical decision theory. The paper deals with a nonMarkovian dynamic programming decision model that includes Markovian decision models and Markov renewal decision models as special cases. The analysis is based on the total cost criterion where the convergence condition on the expected total cost is such that the discounted and the negative (unbounded) case are included. The striking feature of the present model is the fact that the law of motion is not completely known, which leads to a treatment of the model by the approach of statistical decision theory. The assumptions of the present paper are discussed for a sequential statistical decision problem.

Citation

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Manfred Schal. "On Dynamic Programming and Statistical Decision Theory." Ann. Statist. 7 (2) 432 - 445, March, 1979. https://doi.org/10.1214/aos/1176344625

Information

Published: March, 1979
First available in Project Euclid: 12 April 2007

zbMATH: 0417.62002
MathSciNet: MR520251
Digital Object Identifier: 10.1214/aos/1176344625

Subjects:
Primary: 62C05
Secondary: 62M99 , 90C40 , 90C45

Keywords: Compactness and convexity of the space of policies , continuity and stability of the optimization procedure , least favourable a priori distributions , lower semicontinuity of the risk function , minimax and Bayes policies , strict determinateness

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 2 • March, 1979
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