Conditional model order estimation

A new approach to model order selection is proposed. Based on the theory of sufficient statistics, the method does not require any prior knowledge of the model parameters. It is able to discriminate between models by basing the decision on the part of the data that is independent of the model parameters. This is accomplished conceptually by transforming the data into a sufficient statistic and an ancillary statistic with respect to the model parameters. It is the probability density function of the ancillary statistic when adjusted for its dimensionality that is used to estimate the order. Furthermore, the rule is directly tied to the goal of minimizing the probability of error and does not employ any asymptotic approximations. The estimator can be shown to be consistent and, via computer simulation, is found to outperform the minimum description length estimator.