IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i8p1894-1912.html
   My bibliography  Save this article

A unified approach to testing for and against a set of linear inequality constraints in the product multinomial setting

Author

Listed:
  • El Barmi, Hammou
  • Johnson, Matthew

Abstract

A problem that is frequently encountered in statistics concerns testing for equality of multiple probability vectors corresponding to independent multinomials against an alternative they are not equal. In applications where an assumption of some type of stochastic ordering is reasonable, it is desirable to test for equality against this more restrictive alternative. Similar problems have been considered heretofore using the likelihood ratio approach. This paper aims to generalize the existing results and provide a unified technique for testing for and against a set of linear inequality constraints placed upon on any probability vectors corresponding to r independent multinomials. The paper shows how to compute the maximum likelihood estimates under all hypotheses of interest and obtains the limiting distributions of the likelihood ratio test statistics. These limiting distributions are of chi bar square type and the expression of the weighting values is given. To illustrate our theoretical results, we use a real life data set to test against second-order stochastic ordering.

Suggested Citation

  • El Barmi, Hammou & Johnson, Matthew, 2006. "A unified approach to testing for and against a set of linear inequality constraints in the product multinomial setting," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1894-1912, September.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1894-1912
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(05)00096-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. El Barmi, Hammou & Dykstra, Richard L., 1996. "Restricted product multinomial and product Poisson maximum likelihood estimation based upon Fenchel duality," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 117-123, August.
    2. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hammou El Barmi, 2020. "A test for the presence of stochastic ordering under censoring: the k-sample case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 451-470, April.
    2. Chen-Yu Hong & Yu-Wei Chang & Rung-Ching Tsai, 2016. "Estimation of Generalized DINA Model with Order Restrictions," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 460-484, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kwame Addae‐Dapaah & Wilfred Tan Yong Hwee, 2009. "The unsung impact of currency risk on the performance of international real property investment," Review of Financial Economics, John Wiley & Sons, vol. 18(1), pages 56-65, January.
    2. Wojtek Michalowski & Włodzimierz Ogryczak, 2001. "Extending the MAD portfolio optimization model to incorporate downside risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 185-200, April.
    3. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    4. Moshe Levy & Haim Levy, 2013. "Prospect Theory: Much Ado About Nothing?," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 7, pages 129-144, World Scientific Publishing Co. Pte. Ltd..
    5. Michael J. Seiler & David M. Harrison & Pim Van Vliet & Kit Ching Yeung, 2005. "Return Characteristics of State‐Owned and Non‐State‐Owned Chinese A Shares," The Financial Review, Eastern Finance Association, vol. 40(4), pages 533-548, November.
    6. Brogan, Anita J. & Stidham Jr., Shaler, 2008. "Non-separation in the mean-lower-partial-moment portfolio optimization problem," European Journal of Operational Research, Elsevier, vol. 184(2), pages 701-710, January.
    7. Brian Tomlin & Yimin Wang, 2005. "On the Value of Mix Flexibility and Dual Sourcing in Unreliable Newsvendor Networks," Manufacturing & Service Operations Management, INFORMS, vol. 7(1), pages 37-57, June.
    8. Schuhmacher, Frank & Eling, Martin, 2012. "A decision-theoretic foundation for reward-to-risk performance measures," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2077-2082.
    9. Arvanitis, Stelios & Scaillet, Olivier & Topaloglou, Nikolas, 2020. "Spanning tests for Markowitz stochastic dominance," Journal of Econometrics, Elsevier, vol. 217(2), pages 291-311.
    10. Diebold, Franz & Bichler, Martin, 2017. "Matching with indifferences: A comparison of algorithms in the context of course allocation," European Journal of Operational Research, Elsevier, vol. 260(1), pages 268-282.
    11. Hoang, Thi-Hong-Van & Lean, Hooi Hooi & Wong, Wing-Keung, 2015. "Is gold good for portfolio diversification? A stochastic dominance analysis of the Paris stock exchange," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 98-108.
    12. 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.
    13. Thomas Kourouxous & Thomas Bauer, 2019. "Violations of dominance in decision-making," Business Research, Springer;German Academic Association for Business Research, vol. 12(1), pages 209-239, April.
    14. Catarina Roseta‐Palma & Yiğit Sağlam, 2019. "Downside risk in reservoir management," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 63(2), pages 328-353, April.
    15. Hautsch, Nikolaus & Scheuch, Christoph & Voigt, Stefan, 2018. "Limits to arbitrage in markets with stochastic settlement latency," CFS Working Paper Series 616, Center for Financial Studies (CFS).
    16. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2016. "Almost stochastic dominance for risk averters and risk seeker," Finance Research Letters, Elsevier, vol. 19(C), pages 15-21.
    17. Jason Shachat & Lijia Wei, 2012. "Procuring Commodities: First-Price Sealed-Bid or English Auctions?," Marketing Science, INFORMS, vol. 31(2), pages 317-333, March.
    18. Timo Kuosmanen & Thierry Post, 2002. "Nonparametric Efficiency Analysis under Price Uncertainty: A First-Order Stochastic Dominance Approach," Journal of Productivity Analysis, Springer, vol. 17(3), pages 183-200, May.
    19. Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.
    20. Pablo C. Benítez & Timo Kuosmanen & Roland Olschewski & G. Cornelis van Kooten, 2006. "Conservation Payments under Risk: A Stochastic Dominance Approach," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(1), pages 1-15.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1894-1912. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.