Comparison of AIC and MDL to the minimum probability of error criterion

A large variety of model order determination problems involve testing the eigenvalue of a sample covariance matrix to estimate how many of the smallest eigenvalues of the true covariance matrix are equal. Using the theory of multiple hypothesis tests, the author derives the minimum probability of error criterion that is similar to AIC and MDL and is implemented in exactly the same manner, but is designed to minimize the probability of choosing the wrong model order. The basic structure of this test is very similar except for an extra term that increases adaptability and enables this criterion to outperform both AIC and MDL