Statistical test for consistent estimation of causal effects in linear non-Gaussian models

This document contains supplementary material to the article ‘Statistical test for consistent estimation of causal effects in linear non-Gaussian models’, AISTATS 2012. A table of contents is given below. Contents 1 Definitions and background 2 2 Detailed proof of Theorem 1 2 3 Pseudocode of the backward elimination search procedure 6 4 Details on the examples of Figure 1 6 4.1 Model equations and covariance matrices . . . . . . . . . . . . . . . . . . . . . . 7 4.2 The effect of controlling for w in Figure 1 (a) and 1 (b) . . . . . . . . . . . . . . . 8 4.3 Models of Figure 1 (a) and 1 (b) are covariance-equivalent . . . . . . . . . . . . . 10 4.4 Models of Figure 1 (a) and 1 (b) are distinguished for non-Gaussian disturbances . 12 5 An example where rx and ry are independent, but x and ry dependent 13 6 An example of a linearly unfaithful model for which the procedure fails 14 1 

• Type: Journal
• Year: 2012
• Where: JMLR
• Authors: Doris Entner, Patrik O. Hoyer, Peter Spirtes
• Keywords: Causal Effects, Consistent Estimation, Gaussian Models, JMLR 2012, Programming Languages