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Properties of Likelihood Inference for Order Restricted Models

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  • Cohen, Arthur
  • Kemperman, J. H. B.
  • Sackrowitz, Harold B.

Abstract

The most common mode of inference for order restricted models is likelihood inference. See T. Robertson, F. T. Wright, and R. L. Dykstra (1988, "Order Restricted Statistical Inference," Wiley, New York) for an excellent treatment of inference in such models. In this paper we demonstrate that maximum likelihood estimation and likelihood ratio testing are prone to behavior that is somewhat unintuitive and unappealing to our sensibilities for many order restricted models. From a practical standpoint this behavior sometimes is cause enough for us to seek alternative procedures. For restrictions to a simple order cone, likelihood inference is satisfactory. However, if, for example, the restrictions are of the tree order type, umbrella order, star-shaped order, or stochastic order, then likelihood methods seem to have some shortcomings. General results will identify when likelihood methods are potentially wanting.

Suggested Citation

  • Cohen, Arthur & Kemperman, J. H. B. & Sackrowitz, Harold B., 2000. "Properties of Likelihood Inference for Order Restricted Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 50-77, January.
    • Handle: RePEc:eee:jmvana:v:72:y:2000:i:1:p:50-77
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    References listed on IDEAS

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    1. Dykstra, Robert R., 1988. "Trails South: The Wagon-Road Economy in the Dodge City-Panhandle Region. By C. Robert Haywood. Norman: University of Oklahoma Press, 1986. xv + 312 pp. Maps, illustrations, notes, bibliography, and in," Business History Review, Cambridge University Press, vol. 62(1), pages 157-158, April.
    2. Agresti, Alan & Coull, Brent A., 1998. "Order-restricted inference for monotone trend alternatives in contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 139-155, August.
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    Cited by:

    1. Balakrishnan, N. & Beutner, E. & Kamps, U., 2008. "Order restricted inference for sequential k-out-of-n systems," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1489-1502, August.
    2. Manco Gregory V. & Cohen Arthur, 2002. "Inadmissibility Of The Studentized Likelihood Ratio Test For Testing Order-Restricted Normal Means," Statistics & Risk Modeling, De Gruyter, vol. 20(1-4), pages 177-190, April.
    3. repec:jss:jstsof:33:i10 is not listed on IDEAS
    4. Praestgaard, Jens, 2012. "A note on the power superiority of the restricted likelihood ratio test," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 1-15, February.
    5. Cohen, Arthur & Sackrowitz, H. B., 2000. "Properties of Bayes testing procedures in order restricted inference," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 205-209, August.
    6. Youhei Oono & Nobuo Shinozaki, 2006. "Estimation of error variance in ANOVA model and order restricted scale parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 739-756, December.

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