Approximate Non-Similar critical values based tests vs Maximized Monte Carlo tests

Testing in the presence of nuisance parameters is a problem often faced by researchers; consequently, a number of ways are suggested in the literature to manage this situation. Among these, Maximized Monte Carlo (MMC) tests or asymptotically valid MMC (AMMC) tests are becoming popular. The MMC type tests have certain advantages as well as disadvantages. This paper introduces a simple way to obtain Approximate Non-Similar (ANS) critical values using a global optimizer called Simulated Annealing (SA). All three methods are applied in the dynamic linear regression model context. As expected the AMMC approach is certainly less time consuming than the MMC approach. Overall the AMMC approach seems best in terms of power properties; however the ANS approach takes negligible time compared to its competitors. Though the ANS approach controls the sizes well it can be slightly less powerful than its competitors.