Abstract
Structural equation models have been widely used to study causal relationships between continuous variables. Recently, a non-Gaussian method called LiNGAM was proposed to discover such causal models and has been extended in various directions. An important problem with LiNGAM is that the results are affected by the random sampling of the data as with any statistical method. Thus, some analysis of the confidence levels should be conducted. A common method to evaluate a confidence level is a bootstrap method. However, a confidence level computed by ordinary bootstrap is known to be biased as a probabilityvalue (p-value) of hypothesis testing. In this paper, we propose a new procedure to apply an advanced bootstrap method called multiscale bootstrap to compute p-values of LiNGAMoutputs. The multiscale bootstrap method gives unbiased p-values with asymptotic much higher accuracy. Experiments on artificial data demonstrate the utility of our approach.
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