Modified lagrange multiplier tests for problems with one-sided alternatives

A modified Lagrange multiplier test statistic is proposed which takes explicit account of the one-sided nature of the alternative in problems where the null hypothesis specifies that the true value of the parameter vector lies on the boundary of the parameter space. Computation of this statistic requires only the constrained maximum likelihood estimator. Conditions for the consistency of tests based on this statistic are examined and it is shown that the distribution of the statistic is not affected of nuisance parameters are allowed to lie on the boundary of the parameter space.