Abstract
This paper assesses an extension of the method for graphical causal inference proposed by Spirtes et al. and Pearl to nonlinear settings. We propose nonparametric tests for conditional independence based on kernel density estimation and study their relative performance in a Monte Carlo study. Our method outperforms Fischer’s z test for nonlinear settings while subject to the so-called curse of dimensionality. We do show, however, how the latter can be overcome by using local bootstrapping.
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Notes
- 1.
For definition and properties of DAGs see Spirtes et al. (2000: Chapter 2).
- 2.
An example for a collider is displayed in Fig. 6.2: V 2, t forms a collider between V 1, (t − 1) and V 2, (t − 1). In this case
although 
. - 3.
For an introduction to the so-called curse of dimensionality see, e.g., Yatchew (2003, p. 676).
although 
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Chlaß, N., Moneta, A. (2009). Can Graphical Causal Inference Be Extended to Nonlinear Settings?. In: Suárez, M., Dorato, M., Rédei, M. (eds) EPSA Epistemology and Methodology of Science. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3263-8_6
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DOI: https://doi.org/10.1007/978-90-481-3263-8_6
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