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A structure theorem on bivariate positive quadrant dependent distributions and tests for independence in two-way contingency tables

Author

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  • Rao, M. Bhaskara
  • Krishnaiah, P.R.
  • Subramanyam, K.

Abstract

In this paper, the set of all bivariate positive quadrant dependent distributions with fixed marginals is shown to be compact and convex. Extreme points of this convex set are enumerated in some specific examples. Applications are given in testing the hypothesis of independence against strict positive quadrant dependence in the context of ordinal contingency tables. The performance of two tests, one of which is based on eigenvalues of a random matrix, is compared. Various procedures based upon certain functions of the eigenvalues of a random matrix are also proposed for testing for independence in a two-way contingency table when the marginals are random.

Suggested Citation

  • Rao, M. Bhaskara & Krishnaiah, P.R. & Subramanyam, K., 1987. "A structure theorem on bivariate positive quadrant dependent distributions and tests for independence in two-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 93-118, October.
    • Handle: RePEc:eee:jmvana:v:23:y:1987:i:1:p:93-118
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    Cited by:

    1. 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.
    2. Cohen Arthur & Sackrowitz Harold B., 2000. "Testing Whether Treatment Is “Better“ Than Control With Ordered Categorical Data: Definitions And Complete Class Theorems," Statistics & Risk Modeling, De Gruyter, vol. 18(1), pages 1-26, January.

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