Admissible and Bayes decisions with fuzzy-valued losses-Reference-Cited by-同舟云学术

Admissible and Bayes decisions with fuzzy-valued losses

Published:2022-04-01 Issue:2 Volume:32 Page:139-145
ISSN:0924-9265
Container-title:Discrete Mathematics and Applications
language:en
Short-container-title:

Author:

Shvedov Alexey S.¹

Affiliation:

1. National Research University “Higher School of Economics” , Moscow , Russia

Abstract

Abstract Some results of classical statistical decision theory are generalized by means of the theory of fuzzy sets. The concepts of an admissible decision in the restricted sense, an admissible decision in the broad sense, a Bayes decision in the restricted sense, and a Bayes decision in the broad sense are introduced. It is proved that any Bayes decision in the broad sense with positive prior discrete density is admissible in the restricted sense. The class of Bayes decisions is shown to be complete under certain conditions on the loss function. Problems with a finite set of possible states are considered.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics

Link

https://www.degruyter.com/document/doi/10.1515/dma-2022-0013/pdf

Reference25 articles.

1. Blackwell D.A., Girshick M. A., Theory of Games and Statistical Decisions, Wiley Publications in Statistics. New York, J. Wiley & Sons, London, Chapman & Hall, 1954, xi+355 pp.

2. Wald A., “Statistical decision functions”, Ann. Math. Statist., 20:2 (1949), 165-205.

3. Rockafellar R.T., Convex Analysis, Princeton Univ. Press, Princeton, New Jersey, 1970, xviii + 451 pp.

4. Shvedov A.S., Probability Theory and Mathematical Statistics: Intermediate Level, M.: Izd. dom Vysshey shkoly ekonomiki, 2016 (in Russian), 280 pp.

5. Shvedov A.S., “Estimation of means and covariances of fuzzy random variables”, Prikladnaya ekonometrika, 42 (2016), 121138 (in Russian).