## Statistical Science

### 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

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

Digital Object Identifier
doi:10.1214/13-STS429

Mathematical Reviews number (MathSciNet)
MR3300364

Zentralblatt MATH identifier
1331.62277

#### 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

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