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Testing for and against a stochastic ordering between multivariate multinomial populations

Author

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  • Lucas, Larry A.
  • Wright, F. T.

Abstract

Tests for comparing a multivariate response on a control and on a treatment population are considered. It is assumed that each component of the response is a categorical variable with ordered categories. In some situations it may be believed a priori that the treatment has a nondecreasing effect on each component of the response, and in such cases a test of equality of the two populations with a stochastically ordered alternative is of interest. In other situations, the stochastic ordering assumption may be questioned and one would want to test it as a null hypothesis. The likelihood ratio tests, as well as some chi-square analogues, for both of these situations are studied in the one- and two-sample cases. In the latter testing situation, equality of the two populations is shown to be asymptotically least favorable within the stochastic ordering hypothesis. A numerical example is given to illustrate the use of these tests.

Suggested Citation

  • Lucas, Larry A. & Wright, F. T., 1991. "Testing for and against a stochastic ordering between multivariate multinomial populations," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 167-186, August.
    • Handle: RePEc:eee:jmvana:v:38:y:1991:i:2:p:167-186
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    Cited by:

    1. Ori Davidov & Amir Herman, 2011. "Multivariate Stochastic Orders Induced by Case-Control Sampling," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 139-154, March.
    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.
    3. Ori Davidov & Shyamal Peddada, 2013. "Testing for the Multivariate Stochastic Order among Ordered Experimental Groups with Application to Dose–Response Studies," Biometrics, The International Biometric Society, vol. 69(4), pages 982-990, December.
    4. Amiri, Mehdi & Izadkhah, Salman & Jamalizadeh, Ahad, 2020. "Linear orderings of the scale mixtures of the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    5. Li, Hui-Qiong & Tian, Guo-Liang & Jiang, Xue-Jun & Tang, Nian-Sheng, 2016. "Testing hypothesis for a simple ordering in incomplete contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 25-37.

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