## Statistical Science

- Statist. Sci.
- Volume 29, Number 4 (2014), 662-678.

### A Uniformly Consistent Estimator of Causal Effects under the $k$-Triangle-Faithfulness Assumption

#### 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 Bühlmann [*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.

#### Article information

**Source**

Statist. Sci., Volume 29, Number 4 (2014), 662-678.

**Dates**

First available in Project Euclid: 15 January 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.ss/1421330552

**Digital Object Identifier**

doi:10.1214/13-STS429

**Mathematical Reviews number (MathSciNet)**

MR3300364

**Zentralblatt MATH identifier**

1331.62277

**Keywords**

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

#### Citation

Spirtes, Peter; Zhang, Jiji. A Uniformly Consistent Estimator of Causal Effects under the $k$-Triangle-Faithfulness Assumption. Statist. Sci. 29 (2014), no. 4, 662--678. doi:10.1214/13-STS429. https://projecteuclid.org/euclid.ss/1421330552