Variance-component likelihood-ratio test at a boundary
= Variance-component likelihood-ratio test at a boundary
Testing a single nonnegative random-effect variance against zero puts the null on the boundary of the parameter space. In the usual regular increasing-independent-groups limit, the <likelihood-ratio test statistic> has limit $\tfrac12\delta_0+\tfrac12\chi_1^2$, rather than $\chi_1^2$. A finite-sample simulation calibrated for the actual design avoids relying on this asymptotic approximation.