### Abstract

Original language | English |
---|---|

Pages (from-to) | 662-678 |

Number of pages | 17 |

Journal | Statistical Science |

Volume | 29 |

Issue number | 4 |

DOIs | |

Publication status | Published - Nov 2014 |

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### 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

### Cite this

*Statistical Science*,

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

}

*Statistical Science*, vol. 29, no. 4, pp. 662-678. https://doi.org/10.1214/13-STS429

**A uniformly consistent estimator of causal effects under the k-Triangle-Faithfulness assumption.** / SPIRTES, Peter; ZHANG, Jiji.

Research output: Journal Publications › Journal Article (refereed) › Research › peer-review

TY - JOUR

T1 - A uniformly consistent estimator of causal effects under the k-Triangle-Faithfulness assumption

AU - SPIRTES, Peter

AU - ZHANG, Jiji

N1 - Zhang’s research was supported in part by the Research grants Council of Hong Kong under the General Research Fund LU341910.

PY - 2014/11

Y1 - 2014/11

N2 - 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.

AB - 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.

KW - Bayesian networks

KW - Causal inference

KW - estimation

KW - model search

KW - model selection

KW - structural equation models

KW - uniform consistency

UR - http://commons.ln.edu.hk/sw_master/2755

UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-84921458343&doi=10.1214%2f13-STS429&partnerID=40&md5=abeed462ad7686286ca87f0def912319

U2 - 10.1214/13-STS429

DO - 10.1214/13-STS429

M3 - Journal Article (refereed)

VL - 29

SP - 662

EP - 678

JO - Statistical Science

JF - Statistical Science

SN - 0883-4237

IS - 4

ER -