IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v66y2014i2p345-367.html
   My bibliography  Save this article

Qualitative inequalities for squared partial correlations of a Gaussian random vector

Author

Listed:
  • Sanjay Chaudhuri

Abstract

We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several graphical Markov models. Rules for comparing degree of association among the vertices of such Gaussian graphical models are also developed. We apply these rules to compare conditional dependencies on Gaussian trees. In particular for trees, we show that such dependence can be completely characterised by the length of the paths joining the dependent vertices to each other and to the vertices conditioned on. We also apply our results to postulate rules for model selection for polytree models. Our rules apply to mutual information of Gaussian random vectors as well. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Sanjay Chaudhuri, 2014. "Qualitative inequalities for squared partial correlations of a Gaussian random vector," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 345-367, April.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:2:p:345-367
    DOI: 10.1007/s10463-013-0417-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-013-0417-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-013-0417-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nanny Wermuth & D. R. Cox, 2008. "Distortion of effects caused by indirect confounding," Biometrika, Biometrika Trust, vol. 95(1), pages 17-33.
    2. Sander Greenland & Judea Pearl, 2011. "Adjustments and their Consequences—Collapsibility Analysis using Graphical Models," International Statistical Review, International Statistical Institute, vol. 79(3), pages 401-426, December.
    3. Paul Bekker & Jan Leeuw, 1987. "The rank of reduced dispersion matrices," Psychometrika, Springer;The Psychometric Society, vol. 52(1), pages 125-135, March.
    4. Manabu Kuroki & Zhihong Cai, 2006. "On recovering a population covariance matrix in the presence of selection bias," Biometrika, Biometrika Trust, vol. 93(3), pages 601-611, September.
    5. G. O. Roberts & S. K. Sahu, 1997. "Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 291-317.
    6. Tyler J. VanderWeele & James M. Robins, 2010. "Signed directed acyclic graphs for causal inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 111-127, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ryusei Shingaki & Hiroshi Kanda & Manabu Kuroki, 2021. "Selection and integration of generalized instrumental variables for estimating total effects," Statistical Papers, Springer, vol. 62(5), pages 2355-2381, October.
    2. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2016. "Efficient Gibbs sampling for Markov switching GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 37-57.
    3. Strickland, Chris M. & Martin, Gael M. & Forbes, Catherine S., 2008. "Parameterisation and efficient MCMC estimation of non-Gaussian state space models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2911-2930, February.
    4. Ahelegbey, Daniel Felix & Giudici, Paolo & Hashem, Shatha Qamhieh, 2021. "Network VAR models to measure financial contagion," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    5. Pasanisi, Alberto & Fu, Shuai & Bousquet, Nicolas, 2012. "Estimating discrete Markov models from various incomplete data schemes," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2609-2625.
    6. Jos Berge & Henk Kiers, 1991. "A numerical approach to the approximate and the exact minimum rank of a covariance matrix," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 309-315, June.
    7. Pearl Judea, 2017. "A Linear “Microscope” for Interventions and Counterfactuals," Journal of Causal Inference, De Gruyter, vol. 5(1), pages 1-15, March.
    8. Yin, Libo & Ma, Xiyuan, 2018. "Causality between oil shocks and exchange rate: A Bayesian, graph-based VAR approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 434-453.
    9. MacEachern, Steven N. & Peruggia, Mario, 2000. "Subsampling the Gibbs sampler: variance reduction," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 91-98, March.
    10. Håvard Rue & Ingelin Steinsland & Sveinung Erland, 2004. "Approximating hidden Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 877-892, November.
    11. Barone, Piero & Sebastiani, Giovanni & Stander, Julian, 2001. "General over-relaxation Markov chain Monte Carlo algorithms for Gaussian densities," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 115-124, April.
    12. Wong, Jackie S.T. & Forster, Jonathan J. & Smith, Peter W.F., 2018. "Bayesian mortality forecasting with overdispersion," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 206-221.
    13. Yiming Chen & Paul J. Smith & Mei-Ling Ting Lee, 2023. "Causal Inference in Threshold Regression and the Neural Network Extension (TRNN)," Stats, MDPI, vol. 6(2), pages 1-24, April.
    14. Jiang, Zhichao & Ding, Peng, 2017. "The directions of selection bias," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 104-109.
    15. Chib, Siddhartha, 2004. "Markov Chain Monte Carlo Technology," Papers 2004,22, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    16. Jin, Zhumengmeng & Hobert, James P., 2022. "On the convergence rate of the “out-of-order” block Gibbs sampler," Statistics & Probability Letters, Elsevier, vol. 188(C).
    17. Moores, Matthew T. & Hargrave, Catriona E. & Deegan, Timothy & Poulsen, Michael & Harden, Fiona & Mengersen, Kerrie, 2015. "An external field prior for the hidden Potts model with application to cone-beam computed tomography," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 27-41.
    18. Firat Bilgel, 2021. "Infant mortality in Turkey: Causes and effects in a regional context," Papers in Regional Science, Wiley Blackwell, vol. 100(2), pages 429-453, April.
    19. Elena Stanghellini & Eduwin Pakpahan, 2015. "Identification of causal effects in linear models: beyond instrumental variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 489-509, September.
    20. Bianchi, Daniele & Tamoni, Andrea, 2016. "The dynamics of expected returns: evidence from multi-scale time series modelling," LSE Research Online Documents on Economics 118992, London School of Economics and Political Science, LSE Library.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:66:y:2014:i:2:p:345-367. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.