Tuning the EM-test for finite mixture models

There has been rapid progress in developing effective and easy-to-use tests of the order of a finite mixture model. The EM-test is the latest to join the rank. It has a relatively simple limiting distribution and enjoys broad applicability. Based on asymptotic theory, the P-value of the EM-test is approximated via its limiting distribution. The built-in tuning parameter has an important influence on the approximation precision. Thus, choosing an appropriate value for this parameter is important for fully realizing the advantages of the EM-test. In this article, we develop a novel computer-experiment approach to address this issue. Through designed experiments, we derive a number of empirical formulas for the tuning parameter. Extensive validation simulation shows that these formulas work well in terms of providing accurate type I errors. The Canadian Journal of Statistics 39: 389-404; 2011 (C) 2011 Statistical Society of Canada