Nonparametric Detection of Signals by Information Theoretic Criteria: Performance Analysis and an Improved Estimator

Determining the number of sources from observed data is a fundamental problem in many scientific fields. In this paper we consider the nonparametric setting, and focus on the detection performance of two popular estimators based on information theoretic criteria, the Akaike information criterion (AIC) and minimum description length (MDL). We present three contributions on this subject. First, we derive a new expression for the detection performance of the MDL estimator, which exhibits a much closer fit to simulations in comparison to previous formulas. Second, we present a random matrix theory viewpoint of the performance of the AIC estimator, including approximate analytical formulas for its overestimation probability. Finally, we show that a small increase in the penalty term of AIC leads to an estimator with a very good detection performance and a negligible overestimation probability.