Assessing Statistical Reliability of LiNGAM via Multiscale Bootstrap

@inproceedings{Komatsu2010AssessingSR,
  title={Assessing Statistical Reliability of LiNGAM via Multiscale Bootstrap},
  author={Yusuke Komatsu and Shohei Shimizu and Hidetoshi Shimodaira},
  booktitle={ICANN},
  year={2010}
}
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… 
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Slide 8: [1, 2]. Slide 10: [2]. Slide 11: [3]. Slide 15: [4]. Slide 16: [5, 6]. Slide 19: [7, 8, 9, 10, 11, 12, 13, 14]. Slide 21: [14]. Slide 22: [7]. Slide 23: [15, 16]. Slide 24: [7, 17, 18].

References

SHOWING 1-10 OF 13 REFERENCES
A Linear Non-Gaussian Acyclic Model for Causal Discovery
TLDR
This work shows how to discover the complete causal structure of continuous-valued data, under the assumptions that (a) the data generating process is linear, (b) there are no unobserved confounders, and (c) disturbance variables have non-Gaussian distributions of non-zero variances.
Testing Regions with Nonsmooth Boundaries via Multiscale Bootstrap
Abstract A new class of approximately unbiased tests based on bootstrap probabilities is obtained for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is
A new look at the statistical model identification
The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as
Causation, prediction, and search
What assumptions and methods allow us to turn observations into causal knowledge, and how can even incomplete causal knowledge be used in planning and prediction to influence and control our
CONFIDENCE LIMITS ON PHYLOGENIES: AN APPROACH USING THE BOOTSTRAP
  • J. Felsenstein
  • Biology, Medicine
    Evolution; international journal of organic evolution
  • 1985
TLDR
The recently‐developed statistical method known as the “bootstrap” can be used to place confidence intervals on phylogenies and shows significant evidence for a group if it is defined by three or more characters.
An approximately unbiased test of phylogenetic tree selection.
TLDR
It is shown that the AU test is less biased than other methods in typical cases of tree selection, as well as in the analysis of mammalian mitochondrial protein sequences.
An Introduction to the Bootstrap
Bootstrap confidence levels for phylogenetic trees
Evolutionary trees are often estimated from DNA or RNA sequence data. How much confidence should we haveintheestimatedtrees?In1985,Felsenstein(Felsenstein, J. (1985) Evolution 39, 783-791) suggested
Independent Component Analysis
TLDR
Although ICA was originally developed for digital signal processing applications, it has recently been found that it may be a powerful tool for analyzing text document data as well, if the documents are presented in a suitable numerical form.
The Bootstrap and Edgeworth Expansion
1: Principles of Bootstrap Methodology.- 2: Principles of Edgeworth Expansion.- 3: An Edgeworth View of the Bootstrap.- 4: Bootstrap Curve Estimation.- 5: Details of Mathematical Rigour.- Appendix I:
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