Estimation of the probability of informed trading models via an expectation-conditional maximization algorithm

The estimation of the probability of informed trading (PIN) model and its extensions poses significant challenges owing to various computational problems. To address these issues, we propose a novel estimation method called the expectation-conditional-maximization (ECM) algorithm, which can serve as an alternative to the existing methods for estimating PIN models. Our method provides optimal estimates for the original PIN model as well as two of its extensions: the multilayer PIN model and the adjusted PIN model, along with its restricted versions. Our results indicate that estimations using the ECM algorithm are generally faster, more accurate, and more memory-efficient than the standard methods used in the literature, making it a robust alternative. More importantly, the ECM algorithm is not limited to the models discussed and can be easily adapted to estimate future extensions of the PIN model.