Ancestor regression in linear structural equation models

We present a new method for causal discovery in linear structural equation models. We propose a simple technique based on statistical testing in linear models that can distinguish between ancestors and non-ancestors of any given variable. Naturally, this approach can then be extended to estimating the causal order among all variables. Unlike with many methods, it is possible to provide explicit error control for false causal discovery, at least asymptotically. This holds even under Gaussianity where various methods fail because of nonidentifiable structures. These Type I error guarantees come at the cost of reduced power. Additionally, we provide an asymptotically valid goodness-of-fit p-value for assessing whether multivariate data stem from a linear structural equation model.