Kuhn-Tucker,likelihood ratio and Wald tests for nonlinear models with inequality constraints on the parameters

This paper considers the problem of testing statistical hypothesis in nonlinear regression models with inequality constraints on the parameters. First, the Kuhn-Tucker test procedure is defined. Next, it is shown that the distribution of the Kuhn-Tucker, the likelihood ratio and the Wald test statistics converges to the same mixture of chi-square distributions under the null hypothesis. To illustrate these results two examples are considered: (1) the problem of testing that individual effects are missing in an error component model, and (2) the problem of testing equilibrium for a model of markets in disequilibrium.