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Dominance Relations Among Standardized Variables

Author

Listed:
  • Frank Milne

    (Department of Economics, Queen's University, Kingston, Ontario, Canada K7M 3N6)

  • Edwin H. Neave

    (School of Business, Queen's University, Kingston, Ontario, Canada K7M 3N6)

Abstract

This paper examines stochastic dominance relations among discrete random variables defined on a common integer domain. While these restrictions are minimal, they lead both to new theoretical results and to simpler proofs of existing one. The new results, obtained for dominance criteria of any degree, generalize an SSD result of Rothschild-Stiglitz to describe how for any dominance criterion a dominated variable is equal in distribution to a dominated variable plus perturbation terms. If the variables are comparable under FSD the perturbations are downward shift terms, while under SSD (TSD) all but two (three) of the perturbations are zero mean disturbance terms (noise). Under SSD the remaining perturbations are shift terms and under TSD noise and shift terms. However, under either SSD or TSD these remaining terms are identically zero if the variables to be compared have equal means. The paper also finds new proofs of well known results relating dominance criteria to preferences.

Suggested Citation

  • Frank Milne & Edwin H. Neave, 1994. "Dominance Relations Among Standardized Variables," Management Science, INFORMS, vol. 40(10), pages 1343-1352, October.
  • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:10:p:1343-1352
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    File URL: http://dx.doi.org/10.1287/mnsc.40.10.1343
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    Citations

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    Cited by:

    1. Li, Xiaoming, 2008. "Demand evolution in stochastic inventory systems: Riskiness increase," International Journal of Production Economics, Elsevier, vol. 116(2), pages 182-189, December.
    2. Lingxiu Dong & Panos Kouvelis & Ping Su, 2010. "Global Facility Network Design with Transshipment and Responsive Pricing," Manufacturing & Service Operations Management, INFORMS, vol. 12(2), pages 278-298, February.
    3. Dong, Lingxiu & Kouvelis, Panos & Su, Ping, 2013. "Global facility network design in the presence of competition," European Journal of Operational Research, Elsevier, vol. 228(2), pages 437-446.
    4. Chakravarty, Satya R. & Zoli, Claudio, 2012. "Stochastic dominance relations for integer variables," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1331-1341.
    5. Dong, Lingxiu & Kouvelis, Panos & Su, Ping, 2014. "Operational hedging strategies and competitive exposure to exchange rates," International Journal of Production Economics, Elsevier, vol. 153(C), pages 215-229.
    6. Seifert, Ralf W. & Thonemann, Ulrich W. & Sieke, Marcel A., 2006. "Integrating direct and indirect sales channels under decentralized decision-making," International Journal of Production Economics, Elsevier, vol. 103(1), pages 209-229, September.
    7. Miller-Hooks, Elise & Mahmassani, Hani, 2003. "Path comparisons for a priori and time-adaptive decisions in stochastic, time-varying networks," European Journal of Operational Research, Elsevier, vol. 146(1), pages 67-82, April.
    8. Martin A. Lariviere & Evan L. Porteus, 1999. "Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales," Management Science, INFORMS, vol. 45(3), pages 346-363, March.
    9. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.

    More about this item

    Keywords

    stochastic dominance; decision theory; comparing random variables;

    JEL classification:

    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L22 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Organization and Market Structure
    • L68 - Industrial Organization - - Industry Studies: Manufacturing - - - Appliances; Furniture; Other Consumer Durables

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