Asymptotically optimal tests for parametric functions against ordered functional alternatives

There are hypothesis testing problems for (nonlinear) functions of parameters against functional ordered alternatives for which a reduction to a conventional order-restricted hypothesis testing problem may not be feasible. While such problems can be handled in an asymptotic setup, among the available choices, it is shown that the union–intersection principle may have certain advantages over the likelihood principle or its ramifications. An application to a genomic model is also considered.