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Exponential decay of pairwise correlation in Gaussian graphical models with an equicorrelational one-dimensional connection pattern

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  • Marrelec, Guillaume
  • Giron, Alain
  • Messio, Laura

Abstract

We consider a Gaussian graphical model associated with an equicorrelational and one-dimensional conditional independence graph. We show that pairwise correlation decays exponentially as a function of distance. We also provide a limit when the number of variables tend to infinity and quantify the difference between the finite and infinite cases.

Suggested Citation

  • Marrelec, Guillaume & Giron, Alain & Messio, Laura, 2021. "Exponential decay of pairwise correlation in Gaussian graphical models with an equicorrelational one-dimensional connection pattern," Statistics & Probability Letters, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:stapro:v:171:y:2021:i:c:s0167715220303199
    DOI: 10.1016/j.spl.2020.109016
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    References listed on IDEAS

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    1. Harry Joe, 1989. "Estimation of entropy and other functionals of a multivariate density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 683-697, December.
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