Ancestor regression in linear structural equation models

We present a new method for causal discovery in linear structural equation models. We propose a simple ``trick'' based on statistical testing in linear models that can distinguish between ancestors and non-ancestors of any given variable. Naturally, this can then be extended to estimating the causal order among all variables. Unlike many methods, we provide explicit error control for false causal discovery, at least asymptotically. This holds true even under Gaussianity where various methods fail due to non-identifiable structures.