Bootstrap Confidence Intervals in DirectLiNGAM

We have been considering a problem of finding significant connection strengths of variables in a linear non-Gaussian causal model called LiNGAM. In our previous work, bootstrap confidence intervals of connection strengths were simultaneously computed in order to test their statistical significance. However, the distribution of estimated elements in an adjacency matrix obtained by the bootstrap method was not close enough to the real distribution even though the number of bootstrap replications was increased. Moreover, such a naive approach raised the multiple comparison problem which many directed edges were likely to be falsely found significant. In this study, we propose a new approach used to correct the distribution obtained by the bootstrap method. We also apply a representative technique of multiple comparison, the Bonferroni correction, then evaluate its performance. The result of this study shows that the new distribution is more stable and also even closer to the real distribution. Besides, the number of falsely found significant edges is less than the previous approach.