In this talk, we consider structural equation models represented by a mixed graph which encode both direct causal relationships as well as latent confounding. First, we use an empirical likelihood approach to fit structural equation models without explicitly assuming a distributional form for the errors. Through simulations, we show that when the errors are skewed, the empirical likelihood approach may provide a more efficient estimator than methods assuming a Gaussian likelihood. We also profile out certain parameters to reformulate the estimation procedure into a more computationally tractable procedure. Next, we show that when the errors are non-Gaussian, explicit consideration of higher order moments can greatly reduce the class of distributionally equivalent graphs. Using this observation, we develop a search algorithm for DAG discovery. The algorithm uncovers pairwise marginal structure and consistently discovers a single DAG rather than an equivalence class or CPDAG. We then discuss modifications to the algorithm which allow consistent discovery of certain types of mixed graphs. We conclude with a discussion of future work.
Yu-Hsuan S. Wang