A Unified Approach to Likelihood Inference on Linear Inequality Constraints in Contingency Tables

Abstract

In contingency table analysis, a likelihood ratio test for linear inequality constraints is discussed. The restriction condition considered in this article is much more general than usual stochastic order restriction conditions. Asymptotic property of test statistic is shown. Simulation study is conducted to compare the empirical power and size performed via the proposed method and others. Several real data sets are used to illustrate our theoretical result. The idea used in this article can be applied to test the problems with nonlinear inequality constraints.

Keywords:

• Chi-bar-squared
• Inequality constraint
• Likelihood ratio test
• Stochastic order

Mathematics Subject Classification:

• 62H20
• 62H30

Acknowledgments

The authors wish to thank the Editor and the referee for their criticism suggestions that clearly improved this article.

The research is supported in part by NSFC Grant 10771163 and by NSFC #10741002.

Notes

Table 1 is same as the Table 2 in Giancristofaro and Bonnini (2008).

Source: 1991 General Social Survey, National Opinion Research Center, University of Chicago.

is defined by Brunner and Munzel (2000).

W _N -test is the test based on the statistic .