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A simulation study illustrates that our approximate test is more powerful than the Rivers-Vuong test.
In this paper, metamodels based on radial basis functions are applied to approximate test functions known from the literature.
We consider four standard approximate test statistics with and without the common correction of adding 12 to each count.
Then, as an illustration, by considering the model comparison hypothesis defined by the weighted Euclidean norm of moment restrictions, we propose a feasible approximate test statistic to the optimal one and study its asymptotic properties.
Examples and simulation studies are used to compare the operating characteristics between the exact test procedure and three other approximate test procedures.
Simulations indicate that: (a) the approximate test based on the increase of the log-likelihood is helpful in identifying the number of significant sets; (b) the orientation parameters used in the simulation are well retrieved with the proposed algorithm; and (c) the dispersion parameters are more sensitive to the degree of overlap of the simulated joint sets.
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The approximate tests for all of the remaining terms yield significant results.
Owing to a combination of the layout, varying numbers of replicates at each site, and uneven number of individuals in each provenance, F-ratios (Satterthwaite-type approximate tests) were obtained using the TEST option within the RANDOM statement in SAS.
Data were analyzed for significant differences by analysis of variance using approximate tests [ 20].
In addition, for stochastic-based Monte Carlo techniques, researcher must rely on approximate tests of convergence.
Dummy variables will be created for each level and the statistical significance of the regression effects will be tested using the approximate t-test.
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