### Abstract

Spirtes, Glymour and Scheines [Causation, Prediction, and Search (1993) Springer] described a pointwise consistent estimator of the Markov equivalence class of any causal structure that can be represented by a directed acyclic graph for any parametric family with a uniformly consistent test of conditional independence, under the Causal Markov and Causal Faithfulness assumptions. Robins et al. [Biometrika 90 (2003) 491–515], however, proved that there are no uniformly consistent estimators of Markov equivalence classes of causal structures under those assumptions. Subsequently, Kalisch and B¨uhlmann [J. Mach. Learn. Res. 8 (2007) 613–636] described a uniformly consistent estimator of the Markov equivalence class of a linear Gaussian causal structure under the Causal Markov and Strong Causal Faithfulness assumptions. However, the Strong Faithfulness assumption may be false with high probability in many domains. We describe a uniformly consistent estimator of both the Markov equivalence class of a linear Gaussian causal structure and the identifiable structural coefficients in the Markov equivalence class under the Causal Markov assumption and the considerably weaker k-Triangle-Faithfulness assumption.

Original language | English |
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Pages (from-to) | 662-678 |

Number of pages | 17 |

Journal | Statistical Science |

Volume | 29 |

Issue number | 4 |

DOIs | |

Publication status | Published - Nov 2014 |

### Bibliographical note

Zhang’s research was supported in part by the Research grants Council of Hong Kong under the General Research Fund LU341910.### Keywords

- Bayesian networks
- Causal inference
- estimation
- model search
- model selection
- structural equation models
- uniform consistency

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## Cite this

SPIRTES, P., & ZHANG, J. (2014). A uniformly consistent estimator of causal effects under the k-Triangle-Faithfulness assumption.

*Statistical Science*,*29*(4), 662-678. https://doi.org/10.1214/13-STS429